When fewer than 1% of 2014 college-bound high school seniors attain a perfect 800 on the math section of the SAT, you know that you’ve met someone special when he’s achieved that amazing feat before even cracking the teen years. That someone is Shiva Oswal, a precocious 11-year-old from Northern California who recently earned that lofty score as part of a program through Johns Hopkins’ Center for Talented Youth (CTY) called the Julian C. Stanley Study of Exceptional Talent (SET). In fact, the probability of an 11-year-old earning a perfect score is less than 0.01%!
According to its website, SET "was created to help extremely talented students achieve their full potential, and, through its research and advocacy initiatives, to enhance the educational opportunities available for all academically advanced students." Those who qualify through their SAT scores gain access to individualized educational counseling and opportunities to connect with mentors and intellectual peers.
How did Shiva do it? The multi-talented board game designer and aspiring professional soccer player mostly studied on his own by taking SAT practice tests. He kept acing the math section at home, so he felt confident that he had done equally well on the real thing, and indeed, he had. (By the way, Shiva is happy with his performance on the Critical Reading and Writing sections too!) His parents, Arvinder and Vikas, are extremely proud, but they also realize the magnitude of the journey known as raising Shiva.
The Moment You Know Your Child is Gifted
When Shiva was around two years old, his parents noticed that he was able to master abstract concepts and make many logical connections. He often saw patterns and anomalies that others overlooked. For example, having observed that cars had license plates with letters and numbers, he was quick to notice a car with an all-numeric license plate and proceeded to ask numerous questions to understand why. The same thing happened when later that week he saw a car with just letters on its license plate.
As with many gifted children, Shiva enjoys probing a subject thoroughly and persistently asks questions in an attempt to acquire deeper knowledge. "How fast can a cheetah run?" "What will happen if it fights an elephant?" "Is a cheetah faster than Spiderman?" These are just some of the questions that his mother, Arvinder, remembers from a time when two-year-old Shiva was intensely passionate about the swift, spotted feline.
By age four, Shiva was solving math problems in his head. When his preschool teacher asked the class how many hundreds make a million, Shiva promptly responded with the correct answer, 10,000, even though he had never been exposed to the concept of multiplication. At that point, Arvinder and Vikas, were certain that their son was gifted. "We felt a sense of responsibility and were quite unprepared to deal with the needs of a relentlessly curious and intensely gifted child," recalls his mother.
From School to Homeschool
As residents of the Silicon Valley area, the Oswals have access to some of the best schools, public or private, in the United States. During the first few weeks of kindergarten, Shiva was very excited to go to school and usually sat in the front row, eager to learn. Over time, the limited intellectual stimulation led to a decline in his interest in school. By the end of second grade, Shiva frequently announced that lunch and recess were about the only things he looked forward to at school. This is when his parents knew that they needed to look for alternatives.
"While schools did the best they could, they were neither adequately prepared nor widely exposed to what it takes to meet the needs of the gifted child and hence lacked the ecosystem to adequately challenge the gifted mind," explains Arvinder. After a few months of intense reflection and research, they concluded that homeschooling would probably best suit Shiva.
One of the key benefits of homeschooling is the ability to customize an education specific to a child’s passions. Of course, homeschooling has hurdles too. As Shiva’s mom describes, "The primary challenge is that most of the research (to design an optimal experience) rests on the shoulders of parents because designing a sufficiently challenging and engaging learning experience requires an intimate knowledge of the individual child’s passions and strengths."
Resources for Gifted Students
Meeting the educational needs of an extremely bright but young person such as Shiva is no easy task. For his parents, the main difficulty is to continuously find resources of increasing complexity and to pursue these without extinguishing the love of learning. Balance and a sense of what truly matters in life act as guiding principles. "Our hope is that Shiva lives a joyful and fulfilling life while pursuing his passions to the fullest, and we hope he is minimally affected by extraneous factors such as the pursuit of wealth, fame or approbation."
The Oswals have found that the most relevant resources for Shiva have been either online or in classes with small groups of passionate, gifted kids with shared interests.
"Self-paced, online programs such as Elements of Mathematics: Foundations from IMACS are uniquely suited to adequately challenge the mathematically gifted," shares Arvinder. "Our son loves EMF as it allows him to accelerate at his own pace and level up accordingly."
Other online programs that have worked for Shiva include Guinevere’s Gifted Group also known as Online G3. G3 classes are grouped by skill level rather than chronological age to allow asynchronous learners to accelerate as needed. Shiva also loves the Druidawn creative writing program, which taps into "the multidimensional and kaleidoscopic world that resides within the gifted mind."
Live Resources and Events
In addition to online courses, Shiva has benefited from small, live (or live streamed) classes. He loves attending classes taught by Dr. Lucian Sega who encourages gifted students to engage in sustained, rigorous mathematical pursuits. As Vikas and Arvinder explain, "Dr. Sega’s ability to make a broad range of advanced, often abstract mathematical concepts crystal clear is stunning. We find ourselves wishing we could travel back in time to restart our own secondary math education with him!"
For introducing a wide range of math concepts in an engaging way, the Oswals are grateful to Yul Inn of the Fun Math Club. Another extraordinary educator and entertainer who has taught the Oswals much is Dr. Arthur Benjamin. "Our family has enjoyed his Mathemagics shows numerous times. Each time we’ve watched him in action, we gained a new insight, a heightened love for learning or both!"
Other Important Resources
Additional resources can be found through support organizations such as Gifted Homeschoolers Forum, the Davidson Institute for Talent Development, Hoagies’ Gifted Education Page, the TAGMAX listserv and the National Association for Gifted Children.
The responsibility of nurturing a young, gifted child takes heartfelt dedication and constant work to continually build an ever-evolving system of resources and support. It is, without a doubt, a labor of love as only a parent can know it, both the wonderful strides and the worrisome stress. But it is all part of a unique path that each family with a child like Shiva must forge together.
As Shiva’s mom put it beautifully, "An important part of what we do has to do with ‘the journey’. The journey has not been delegated. The fondest part is that we are traveling on this journey together. We are constantly amazed at how far a child can go when allowed to freely pursue a passion-centric learning approach. It’s been a joy to see Shiva surprise us every day with out-of-the-box solutions. We are very grateful for all that we are learning together as a family because we often satisfy curiosities rather than march to fulfill an external mandate or to earn a grade."
Editor’s Note: Shiva’s parents granted IMACS permission to disclose his status as a Davidson Young Scholar and as a participant in the CTY SET program.
The Institute for Mathematics and Computer Science (IMACS) recently released its first online algebra course, Algebra: Groups, Rings and Fields. This is the tenth course in the Elements of Mathematics: Foundations (EMF) program for talented secondary school students. Our latest self-paced offering has generated a fair amount of inquiries from parents seeking options for their mathematically advanced child. The answers to some of those questions can be found in the FAQ at elementsofmathematics.com. IMACS responds to others, which have been consolidated by topic, in this week’s blog post.
Q: My child aced pre-algebra and is ready for algebra. Why can’t I just enroll her in the first EMF algebra course?
When people use the term "algebra," they’re usually talking about high school algebra or what mathematicians call "elementary algebra." By contrast, EMF teaches the kind of algebra that a mathematics major at university learns called "abstract algebra." A student who has mastered pre-algebra is, no doubt, ready for high school algebra. However, this same student, no matter how talented, is simply not ready to jump directly into abstract algebra.
Why? Just as success in high school algebra is built on the foundation laid by elementary school math up through pre-algebra, success in abstract algebra requires a strong foundation in various mathematical structures and reasoning techniques that are rarely taught outside of a university setting. This important foundation is built up through the first nine courses of the EMF program. In fact, one might think of these early courses as constituting "pre-abstract algebra." As such, they are an integral part of the EMF program and essential to success in the later courses.
In case you’re wondering, students who complete the EMF algebra courses will have learned all of elementary algebra and be able to solve any high school algebra problem with ease. But they will also have learned a great deal more and be well-prepared to study the high-level mathematics that is at the heart of important disciplines such as particle physics and cryptography.
Q: What if my child already took high school algebra and geometry? Is there anything left for him to learn in EMF?
As IMACS principal founder and EMF co-author, Burt Kaufman, once wrote, "It is surely a sad state of affairs that in the traditional high school curricula, the student encounters very few, if any, mathematical ideas that postdate the seventeenth century. … It would be ludicrous if an English curriculum for the high school never contemplated confronting the student with a piece of literature written after Shakespeare."* That’s one key reason why the EMF curriculum was created—to teach modern mathematics to talented, young students who are capable of benefiting from advanced material that goes beyond the outdated math curricula used in schools.
Naturally, more experienced students will find some of the EMF material familiar, but EMF approaches these topics from a far more sophisticated standpoint. Between the new mathematical structures and techniques for reasoned argument that they will be learning, there is much for these students to gain in EMF if they are motivated to learn real mathematics as opposed to just school math.
Q: We tried other math programs for advanced kids, but they just seemed to be about going faster or preparing for competitions. That’s not working for our son who’s more of a deep thinker. I’ve heard that EMF takes a different approach. Can you explain?
First, a pair of quotes:
—Jim Simons, Mathematician and Founder of Renaissance Technologies
—Jo Boaler, Professor of Mathematics Education, Stanford University
The competition-inspired approach to math has its merits. But it’s hardly the only approach worthy of mathematically talented kids. The gifted population is filled with individuals who have exceptional talent and prefer to take their time. EMF is an ideal option for these students because the program is self-paced and encourages patience in coming to a deeper understanding of complex and beautiful ideas. At the same time, we’ve had numerous EMF students who also enjoy and excel at competition math. In fact, in situations where speed is of the essence, the non-standard mathematics to which EMF students are exposed gives them a distinct advantage over others who are seeing these ideas for the first time during a competition.
Q: You say that EMF is "mathematician math," and that it’s taught the way a math major at university would be taught. That’s nice, but what are the benefits for a talented child who has no interest in being a math major, let alone a mathematician?
Before your child writes off being a math major completely, especially if that choice is based on experiences with school math, consider the following:
—Keith Devlin, Professor of Mathematics, Stanford University
Whether your child decides to pursue a math major or not, there are several important skills that the EMF approach to mathematics teaches. As with all IMACS programs, EMF fosters the development of logical reasoning skills in young students. While some people believe that logic is cold and inhibits creativity (think: Star Trek’s Spock!), our experience teaching the EMF curriculum over the past 30+ years suggests otherwise. To the contrary, we have found that when IMACS students are equipped with the logic skills to construct their own well-reasoned arguments and critique those of others, the clarity of thought that this produces unleashes creative and innovative ideas that were previously unfocused or muddled.
Which brings us to how EMF encourages creative thinking. As Professor Devlin reminds us, mathematics is a creative discipline. The fact that what passes as "math" in schools is devoid of creativity should not be taken as evidence that true mathematics is indifferent to creative thinking. School math tends to take a "tell-then-drill" approach where the teacher states a rule and then students apply the rule to umpteen haphazard problem sets. By contrast, EMF uses carefully constructed exercises and interactive technology to guide students to their own "discovery" of mathematical results. To be successful in EMF, a student simply must think creatively in order to cross the bridge from keen mathematical observations to the "A-ha!" moments of intuitive understanding. And when these moments happen, the joy and pride of having climbed the intellectual mountain are profound.
Another skill that EMF promotes is abstract thinking. Imagine a world in which most jobs involve people interacting with tangible objects in the present. Perhaps you envisioned the Industrial Revolution, a time when mechanical inventions led to an explosion in manufacturing. Today, we find ourselves amidst a Knowledge Revolution wherein technological inventions mean that well-paying jobs require abstract thinking about intangible ideas such as code. This is obviously true in tech, but because tech touches every industry now, it’s also true for wide-ranging fields from medicine to music to law to film. It’s the question on many people’s minds: Are you going to design and program the robot, or will you be replaced by the robot? Whatever career your child pursues, he or she will almost certainly need to think abstractly. Abstract thinking is fundamental to the study of genuine mathematics, which is what EMF teaches.
Is EMF right for your child? IMACS created a 30-minute, online Aptitude Test to help prospective parents and students answer this question. Register to take the FREE test at elementsofmathematics.com. Extensive sample content from actual EMF courses is also available at elementsofmathematics.com.
LIMITED TIME OFFERS: Save 25% when you enroll on or before March 15, 2015 in the first EMF course (Operational Systems) or in the first ten courses (EMF Course Pack 10). Visit elementsofmathematics.com to enroll today!
* Kaufman, Burt, Jack Fitzgerald, and Jim Harpel. MEGSSS in Action. St. Louis: CEMREL, Inc., 1981.
This month’s IMACS Blog features Shiva Oswal, one of the top performers in our Elements of Mathematics: Foundations (EMF) self-paced, online program for talented secondary school students. Shiva has been enrolled in EMF since the beginning when IMACS introduced the first course of the series in late 2012. As his mom told us, “[O]ur son is an avid user of online educational resources. I recently asked him to pick his favorite online course. He answered, ‘most definitely EMF, by a wide margin’.”
Please tell our readers a little bit about yourself and what you enjoy doing.
I’ll be turning 11 soon, and I love the EMF courses! As a history buff, I really enjoy reading about decisive battles in world history. I also like playing board games and computer games. Right now my favorite board game is Robo Rally, and my favorite computer game is Castle Empire. On the weekends, I participate in Live Action Role-Playing (LARP) events. Soccer is another activity I enjoy. My favorite position is goalie.
You’ve done some amazing things already at a young age. Tell us about the accomplishments of which you are most proud.
This year, I scored 24 out of 25 to earn a gold pin in the Mathematical Olympiads for Elementary and Middle Schools (MOEMS), and was named MOEMS “Mathlete of the Year” for my geographic region. I also invented a new board game called “Minetrap”. I am currently working on publishing my game. If you would like updates, email me at shivarasul [at] gmail [dot] com. Finally, I completed the first seven EMF courses and am almost finished with the eighth course. I am excited to start the ninth course, Number Theory soon.
How did you become interested in mathematics?
When I was in preschool, I was doing multiplication. When math in regular school became too easy, I decided to homeschool so I could work on challenging math problems and concepts.
How did you become interested in taking EMF courses?
My mom encouraged me to try the EMF courses, and I’ve been hooked ever since.
What are the things you enjoy most about EMF?
I like the way concepts are explained. The format of EMF courses, reading followed by exercises, helps check my understanding. The interactive tools such as The String Game make learning math fun. Also the point system (i.e., ability to level up based on mastery of material) makes EMF addictive.
What are some ways in which your EMF experience has had a positive effect on your academic and non-academic pursuits?
When I did my first EMF course, Operational Systems, I was very new to the field. I learned a great deal about operational systems and modular arithmetic after I completed this course. I have grown by leaps and bounds as an analytical thinker as EMF courses force me to think. The program has also helped me improve my skills at strategy games like chess.
What kinds of things do you see yourself doing in the future?
First and foremost, I would like to complete all 15 EMF courses. I hope to get to Calculus before I’m 13 years old. I am also working on becoming a professional soccer player.
Thank you, Shiva, for sharing your story and congratulations on your amazing accomplishments!
Half Price Holiday Sale: Try the first course, Operational Systems, at 50% off the regular price when you enroll on or before December 20, 2014.
Bundled Savings: Save 25% on EMF Course Pack 9, which includes the first nine courses, when you enroll on or before December 20, 2014.
Once upon a time, there was a bright student who first came to IMACS when he was already in high school. He was interested in learning to program and had heard high praise for our University Computer Science courses. The class began smoothly as teacher and pupil progressed through the principles of computational thinking. This student, who was used to conquering schoolwork with his brain tied behind his back, slayed the early exercises with ease. As the assignments quickly became more challenging, however, he found himself unaccustomed to the effort of intellectual struggle. One day, our earnest student declared to his IMACS instructor that a certain programming problem was simply impossible to solve! Our wise and experienced teacher considered this student with a measured gaze and pointed out, “But you’ve only thought about it for three minutes.” The student, quite politely, seriously, and honestly replied, “Well, yeah.” If only he had started IMACS when he was younger. The moral of the story: The earlier the experience of true intellectual challenge, the stronger the will of the mind to persevere. (In other words, enroll your elementary school child in IMACS today!)
This month the IMACS Blog caught up with Azzara Nincevic, who has been a star student at IMACS for seven years now. Azzara enjoys reading, drawing, and classical ballet. Although she dances at least 12 hours per week and performs throughout the year, she always finds time for IMACS.
“When I began IMACS in first grade, I immediately loved it.” Azzara says. “Having taken an interest in math, I quickly learned the traditional material and was looking for more challenging enrichment. When I attended class at IMACS, all of the problems were thought-provoking.”
As a member of her school’s math team, Azzara attends competitions such as MATHCOUNTS and Mu Alpha Theta where her IMACS background has been an invaluable asset. As Azzara describes it, “The IMACS curriculum helped me to develop logical thinking skills and the ability to quickly solve math problems, which are key to succeeding at math competitions.”
“With the preparation that IMACS gave me, I was able to score a 5 on the AP® Computer Science exam as a seventh grader.”
While Azzara’s achievements in mathematics and ballet, by themselves, are enough to impress anyone, it’s her recent performance on the AP® Computer Science A exam that readers will recognize as a rare feat. Soon after starting IMACS Math Enrichment program, Azzara enrolled in our Computer Enrichment & Virtual Robotics class where she developed a great interest in programming. Over the years, she continued with IMACS University Computer Science (UCS) track, which culminates in our AP® Computer Science: Java Programming course.
AP® exams are typically administered to high school students, but at the time that Azzara was ready for APCS, she was only just entering seventh grade. That didn’t deter her. “After inquiring, my mom and I found out that there is no minimum age requirement for an AP® exam, so I registered. With the preparation that IMACS gave me, I was able to score a 5 on the AP® Computer Science exam as a seventh grader.”
With such a busy schedule, Azzara appreciates that one of the greatest benefits of IMACS is that the computer science and logic programs are accessible online and self-paced. “I was able to excel at my own pace and access the IMACS curriculum anytime and anywhere.”
What does the future hold for Azzara? “I am entering the eighth grade with a greater passion for and interest in math and computer science. IMACS made me realize that I would like to pursue computer science in college and after. The fundamental skills that I have learned in the UCS courses and the logical thinking skills I have learned in the Math Enrichment and Mathematical Logic courses give me the advantage I need to be successful. As such, I plan to continue with IMACS in the upcoming years.”
Homeschooling is growing in the United States, having shifted from the “fringe” toward the mainstream. In January 2014, the National Home Education Research Institute (NHERI) estimated that there were 2.2 million1 K-12 home-educated students in the US, up from an estimated 1.5 million2 in 2007. According to the NHERI, one of the most common reasons that families choose homeschooling is to “customize or individualize the curriculum and learning environment for each child.” Not surprisingly, families with gifted children make up a significant part of the current homeschool movement.
If you thought that homeschooling meant having to teach your child all subjects on your own while sitting together at the kitchen table until you drive each other crazy, think again. Modern technology has opened up a world of educational opportunities. Online courses abound in every subject you could imagine. Social media allows homeschool parents to connect and form co-ops where they can share the work of teaching. Some public school districts offer classes taught by credentialed teachers several days a week at a homeschool campus. And numerous educational organizations offer local day classes for homeschoolers, such as the IMACS Homeschool Program. The job of teaching no longer has to be carried out solely by the homeschool parent.
Homeschooling also supports the need that many gifted students have to be self-directed learners. As eIMACS student and 2011 US Girls Junior (U21) Chess Champion Rachel Gologorsky said, “I recognized this as an excellent opportunity to have a say in my education.” In addition to allowing her to participate in the decision-making process, homeschooling provides Rachel with the flexibility she needs to develop her incredible chess talent, including travelling to national and international competitions.
Another oft-cited benefit of homeschooling is the freedom to custom-tailor an educational program that is matched, subject by subject, to a student’s abilities, learning style, and processing speed. Children can fully develop their strongest areas by going as deeply into a subject as they wish or by advancing as quickly as they are able while getting the appropriate level of support they need in other areas. This can be a good fit for many gifted children who, contrary to common misconceptions, are not always the fastest or highest achieving in every subject.
Consider what mathematician and hedge fund billionaire, James Simons, said in a recent New York Times article: "I wasn’t the fastest guy in the world," Dr. Simons said of his youthful math enthusiasms. "I wouldn’t have done well in an Olympiad or a math contest. But I like to ponder. And pondering things, just sort of thinking about it and thinking about it, turns out to be a pretty good approach." Today, a student like the young Dr. Simons can explore deep ideas in mathematics on his or her own schedule with self-paced, homeschool-friendly options such as eIMACS and Elements of Mathematics: Foundations.
A wealth of advice on homeschooling is available online, from helping families decide whether it is a feasible option to helping homeschooled high schoolers apply to college. Speaking of college, did you know that elite universities such as Stanford, MIT, Caltech, Princeton and Yale have sections on their websites dedicated to admissions information for homeschoolers? Homeschooled students are hot! As one Stanford Alumni Magazine article explained, “Stanford has found that the brightest homeschoolers bring a mix of unusual experiences, special motivation and intellectual independence that makes them a good bet to flourish on the Farm.”
While homeschooling has its advantages, it is not for every family. The benefits described above often come with meaningful sacrifices that should be considered carefully. Many families are already well-served by their local public or private schools. But for those who need a more customized education for any number of reasons, including giftedness, homeschooling today offers many options that make this path highly accessible.
If you are considering homeschooling your gifted child, start by visiting the following informative websites:
Families in the South Florida area may also find The Home Educator Magazine to be a helpful resource for local information.
1 From http://www.nheri.org/research/research-facts-on-homeschooling.html
2 From http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009030
It’s graduation time! The summer ritual of getting kids ready to send to college is around the corner. Mini-fridge, check. Shower caddy, check. Good study habits, hmmm. Surprisingly, developing good study habits before entering college is something that many talented children and their parents overlook. It’s easy to understand how this oversight happens when you realize that bright students often don’t need to study. That’s because their schoolwork isn’t challenging and requires minimal effort to receive high grades. Kids who are used to coasting like this hit reality in a big and stressful way when they encounter the rigor and higher expectations of college. But it doesn’t have to be like this. Helping your child build good study habits well before college is essential to their long-term success and happiness. You don’t develop your slice backhand by hitting tennis balls that are tossed straight at you. Likewise, you don’t develop strong study skills by “learning” easy material! It’s also important to let your child know that the effort he or she puts into intellectual pursuits, not just the outcome, matters to you. Failure should not only be an option but an understandable expectation when aiming high. As Thomas Edison said, “I have not failed. I’ve just found 10,000 ways that won’t work.” By encouraging a positive mindset and providing your child with challenging opportunities designed to stretch the talented mind, you’re well on your way to checking off the box for good study habits and many other skills that your child will need before, during and after college.
The new school year is now a month old. By this time, most children who attend a public K-12 school in the US will have experienced the new Common Core State Standards in Mathematics (CCSSM). On the one hand, IMACS is pleased to see that key elements of the teaching philosophy we have lived by for more than 20 years are reflected in the Common Core Standards for Mathematical Practice. For a variety of reasons, however, we maintain a healthy amount of skepticism about whether the implementation of the CCSSM will lead to meaningful, positive change in mathematics education, particularly for our most talented youth.
Common Core Was Not Designed for Gifted Kids
First, the CCSSM was not designed with exceptional kids in mind. The official Common Core Web site states plainly that:
“The Standards set grade-specific standards but do not define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations.”
The Web site further acknowledges that Common Core, like its predecessors, cannot adequately address the unique needs of individual learners:
“No set of grade-specific standards can fully reflect the great variety in abilities, needs, learning rates, and achievement levels of students in any given classroom.”
As to what educators should do about serving the diverse needs of a student body, Common Core guidance leaves them with unresolved internal conflict, offering both:
(i) “Learning opportunities will continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.”
(ii) “The Standards should be read as allowing for the widest possible range of students to participate fully from the outset, along with appropriate accommodations to ensure maximum participaton (sic) of students with special education needs.”
[Note that Common Core does not include gifted children as an example of “students with special education needs.”]
But children in the right-hand tail of the distribution do have special education needs. Whether due to a failure to understand this fact, budgetary pressure, or some other constraint, some school districts seem to be latching on to (ii) above, using the arrival of Common Core as a reason to reduce or eliminate services or accommodations for gifted students. Should this become a national trend in education policy, our country will surely suffer as the majority of gifted children who rely on public education are left without appropriate alternatives.
What About Creative Problem Solvers?
Notwithstanding the potential for improving the thinking skills of typical students, the CCSSM are simply not built to inspire or nurture the creative problem solver. The unfortunate embracing of computerized testing as a cheap means of measuring “learning” — consequently resulting in a culture of teaching to the test — has made the K-12 classroom a place to dread for many unique thinkers. The plan to continue use of computerized testing under the new standards suggests that the non-standard thinker may still be out of place in the Common Core classroom.
IMACS recently asked Gerald R. Rising, SUNY Distinguished Teaching Professor Emeritus at the University at Buffalo, how he thought the CCSSM would affect mathematics education for bright children, to which he replied, “Any imposed curriculum can have a depressing effect on special programs for gifted students.” He also shared the following anecdote about the limits of standardized testing:
“On one of the tests appeared the trivial-sounding question that went something like this: ‘A workman seeks to pass a 20-foot long board through an opening with rectangular 6-foot by 8-foot cross-section. What is the maximum width of the board that is possible?’ The answer choices were: 8 feet, 9 feet, 10 feet and 11 feet. Several of our students answered 9 feet, because the board would necessarily have some thickness that would prevent a 10-foot wide board from passing through the opening. They lost full credit for thinking that was perfectly reasonable but that did not fit the professional test constructor’s overly simplistic model.”
IMACS has been delivering courses and administering tests online to bright and creative children for over 15 years, so we know a thing or two about designing effective computerized assessments of high-level thinking skills. Let’s just say that it takes tremendous creativity, foresight, and a deep understanding of how to leverage the power of technology. If high-stakes testing is here to stay, as it appears to be, we sincerely hope that the consortia working on Common Core-aligned assessments will find ways to reward (or at least not penalize) creative problem solvers.
Inadequate Investment in Training
Common Core marks a major change in teaching philosophy for math education in the US. The intent is to move away from just teaching procedural skills by giving equal weight to conceptual understanding. Teaching math with an emphasis on thinking and understanding, however, is not something one becomes proficient in after a few hours of training, which is all that many districts have provided to their teachers.
Such a radical shift in mindset can be especially challenging for some who have taught math with a completely different focus for many, many years. This is not to say that teachers are incapable of learning to teach a new way — quite the contrary. But, as with any field undergoing fundamental change, extensive training and professional development are necessary if districts and schools want a successful implementation of Common Core. So far, the evidence suggests that they cannot or will not be making that investment.
“Common Core” Textbooks In Name Only
Many of the textbooks currently on the market that say they are aligned to the Common Core standards were developed before the creation of the CCSSM. Note the example below of pages from old and new versions of a math text currently being used in California. The pages on the left were from the edition published in 2009, the year before states began adopting the CCSSM. The pages on the right are from the current edition that proclaims “Common Core” on the cover. (Click on an image to enlarge.)
Furthermore, such textbooks often only align to the specific content skills listed in the CCSSM rather than subscribing to the overall philosophy of the CCSSM. Many that claim to be aligned to the CCSSM do not include problems or tasks that involve the higher-level thinking skills that are supposed to be measured by the new Common Core standardized tests being developed.
Awareness and Advocacy Are More Important Now Than Ever
What does all this mean if you are the parent of a talented child? Probably more work for you. Just over a month ago, nearly two-thirds of respondents to a poll on education said they had never even heard of Common Core! So, if you’re thinking that someone else will speak up first, don’t count on it. Advocacy for a gifted student has never been easy given the lack of awareness and amount of misinformation about their unique educational needs. With the potential for Common Core to bring more harm than good to the education of exceptionally bright kids, it is more important now than ever to be heard.
This month the IMACS Blog speaks with IMACS student, Fiona Brady. According to Fiona’s mom, Susan, “IMACS was the first time Fiona had encountered a community of teachers and learners who were excited to hear her ideas and creative ways of problem solving.” After the Brady family moved out of the area, Fiona continued taking courses through our distance-learning program, eIMACS.
Having studied University Computer Science and AP® Computer Science through eIMACS (and scoring a 5 on the AP® exam), Fiona was able to pick up the Python programming language* when she encountered it at a summer mathematics camp at the University of Chicago with students several years older than she.
For students as talented as Fiona, homeschooling and early college courses often make the most sense as they and their families seek educational options that provide enough challenge, flexibility and inspiration to help them reach their highest potential. Let’s hear what Fiona has to say about pursuing this path:
Please tell our readers a little about yourself.
I’m turning sixteen this fall and I’m in tenth grade. I’m a second degree black belt in Tae Kwon Do, and I enjoy figure skating and horseback riding. I don’t feel like this gives a real image of me, but there it is. I enjoy making things with cardboard and duct tape, but definitely not wallets. I’ve made my Halloween costumes for the last few years. The year before last, I was Medusa. I wore a snake hat that I built in my bedroom and needed to turn sideways to get out. I have since learned that on some occasions it is important to get dressed outside of your room. When I’m not doing math, I love reading.
You are homeschooled and also taking college classes at Northwestern University. What is it like to do both? How do you balance the academic workload, extracurriculars and time with friends and family?
Homeschooling is not like regular school because there is no large division between having fun and learning. So I don’t balance it. However, when I have a large assignment due, my mom probably doesn’t see me for two days. My extracurricular activities — skating, horseback riding and Tae Kwon Do — force me to do something active. I also enjoy volunteering at the barn where I ride because they work with children with special needs. Our three dogs keep me pretty busy too, especially my own puppy, Mole (named because the white fur around his nose made him resemble a star-nosed mole when I first got him).
What circumstances led you to take university classes?
I have always liked math, so I started taking more than one math class a year. In my eighth grade year I took five. After that, I sort of ran out of other options. I participate in the University of Chicago’s Young Scholars Program, which is led by Professor Paul Sally. He and others at Chicago gave me advice and helped to set up a meeting with the head of the Northwestern Math Department, Professor Mike Stein. Professor Stein gave me permission to sit in on the courses, and introduced me to the professors.
Which classes are you taking at Northwestern? How did your IMACS courses prepare you for those classes?
Last year I took a course on Abstract Algebra and one on Multivariable Calculus and Linear Algebra. This year I am taking Physics and Analysis. IMACS was the first place where I encountered the idea that to learn something you have to own it; that is, you have to be able to form a picture of it in your head, and you need to be able to construct it from basic principles. In the IMACS computer science classes I took, you really needed to do that, otherwise you would get lost in the middle of writing a program and forget what you were doing. IMACS Logic for Mathematics is a continuation of that because it is constructing the basic principles of mathematics, which are skipped over in most high school classes (but assumed to be known in college courses).
[Editor’s Note: This past spring, Fiona received an award from the Northwestern Mathematics Department for outstanding achievement in mathematics by a high school student.]
What advice would you give to young students who are thinking about taking university classes before they officially enter college?
Ask your teacher questions. I’ve had people in classes ask me questions, instead of asking the teacher. That’s a really big mistake, and it’s an even worse mistake to make in college because the professors are amazing. One of the things I most admire about the professors I’ve had at Northwestern is the unshakably solid understanding they have of the material. Also, if your professor asks the class a question and you think you know the answer, you should raise your hand. Even if your answer is not correct, that just gives you the opportunity to ask a question and figure out what you don’t understand before you try to learn something that builds on it or have a test.
What do you see yourself doing in the future?
I have three more years before I go to college and I want to keep taking classes and learning more. Being a professor sounds like an interesting career. (Being a stuntman does, too, but I don’t think I’ll pursue that.)
*IMACS added Python to University Computer Science II in November 2012 after Fiona had completed the course.
UPDATE, May 27, 2014: IMACS student, Peyton Robertson, impressed President Barack Obama at today’s fourth annual White House Science Fair. Watch Peyton with President Obama starting around the 4:35 mark of this video.
UPDATE, October 9, 2013: Congratulations to IMACS student, Peyton Robertson, on winning the title of “America’s Top Young Scientist,” $25,000 and a trip to Costa Rica! Watch Peyton’s winning moment.
From the moment you meet IMACS student, Peyton Robertson, you can’t help feeling that he is one of those bright, young people who is going to leave his mark on the world in a big way. His creative ideas and energy seem boundless. His smile and enthusiasm are infectious. And he’s just 11 years old!
Most recently, Peyton entered the 2013 Discovery Education 3M Young Scientist Challenge and is one of only 10 finalists (and the youngest) in this prestigious national science competition for 5th through 8th graders. The Young Scientist Challenge encourages students to explore science and innovation during the pre-teen years when interest in math and science typically starts to decline.
Peyton’s project, SOS: Sandless Operational Sandbags, focuses on developing a more effective and less costly sandbag design to protect against damage from saltwater flooding. As Peyton notes in his finalist video, 80% of the $43 billion dollars worth of flood damage caused since 2005 has been from saltwater flooding. Peyton’s native Florida is at risk for hurricane-driven saltwater flooding every year. So he’s decided to do something about it by re-engineering the basic tool of flood control: the sandbag.
The design of traditional sand-filled sandbags means that they are heavy, difficult to transport and, when stacked, leave gaps through which water readily flows. Peyton’s design uses a thin, expandable polymer to keep his bags light and easy to transport. He also pre-fills his bags with enough salt so that when it dissolves, the salt content of the solution inside is higher than that of seawater, helping to keep the seawater from penetrating the bags. Finally, Peyton uses an ingenious interlocking design to minimize the gaps between the bags when they swell. When the water recedes and the bags dry out, they return to their thin, easily transported and stored form, ready for use during the next storm.
IMACS is so proud of Peyton and delighted to count him as one of our many exceptional students. When we asked Peyton’s mom, Shannon Robertson, to describe the influence that IMACS has had on his education, this is what she had to say:
“I’ll never forget our first encounter with IMACS. My son, who was three at the time, was with me at a school activities fair. He had a strong aptitude for math, so I wanted to learn more about the IMACS program. I immediately loved their focus on math and logic education. Even though we were not able to immediately enroll in the program, IMACS counseled us and gave us outstanding advice on other programs for gifted students.
Today, my son has been a part of IMACS for four years and frequently comments on how IMACS has helped him solve word problems or logic puzzles at school. IMACS fills in many of the gaps that exist in his school-based math curriculum and has given him a deeper understanding of the math that he has learned independently.
My twin girls are also in IMACS. We wanted to establish a strong foundation in logical thinking for them at an early age. After just a few months, we saw a leap forward in their math skills and critical thinking.
All three of our children look forward to their IMACS class time and dive into the supporting assignments after class. IMACS creates a uniquely fun and challenging experience for gifted students through their innovative curriculum and supportive staff. It has been an essential component of the education program for our children.”
Congratulations, Peyton! Your friends at IMACS wish you the best in the finals of the 2013 Young Scientist Challenge.
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