The Modern Face of Homeschooling: Spotlight on Gifted Education


August 7, 2014 Filed under: Gifted And Talented,Parenting IMACS Staff Writer @ 1:00 am

Homeschool classes in math, computer science and more for gifted children who enjoy fun, academic challenges.

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.

Homeschool classes in math, computer science and more for gifted children who enjoy fun, academic challenges.

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.

Homeschool classes in math, computer science and more for gifted children who enjoy fun, academic challenges.

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.

Sources:
1 From http://www.nheri.org/research/research-facts-on-homeschooling.html
2 From http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2009030


Need a homeschool-friendly option to challenge your talented child? The IMACS Homeschool Program is perfect for local South Florida students in grades 1-9. Middle and high school-age students looking for self-paced, online options may enroll in eIMACS or Elements of Mathematics: Foundations. Like IMACS on Facebook for the latest information about our local classes and online courses.
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The Negative Effects of Homework Help


July 10, 2014 Filed under: Parenting IMACS Staff Writer @ 1:00 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.

In The New York Times article, “But I Want to Do Your Homework,” author Judith Newman describes how she was driven, over her 12-year-old son’s objections, to help him ace his literature essay, only to earn a dismal grade. Her admission may sound familiar to many well-intentioned parents who believe they are doing what’s best for their child’s long-term success. Unfortunately, that’s not the case as Newman points out:


“Sociologists at the University of Texas at Austin and Duke University assessed the effect of more than 60 kinds of parental involvement on academic achievement. Read it and weep, helicopter parents: Across age, race, gender and socioeconomic status, most help had neither a positive or negative effect, and many kinds drove down a kid’s test scores and grades. One of the biggest culprits? Homework help.”

It’s not a crime for parents with talented kids to envision them accumulating straight A’s and academic awards on their way to reaching their full potential. However, knowing that it’s okay to be wrong gives children the permission they need to take the kinds of intellectual risks required in order to achieve great things, as Newman learned:


“When I confessed my sins to Michael Goldspiel, my son’s beloved assistant principal … he summed up the problem better than I could. “Being wrong is part of the process of understanding,” he said. “Going out on a limb, being willing to take a chance, is a critical skill not just for homework, but for life.” He couldn’t be more correct.”

IMACS provides bright students with a fail-safe learning environment that is both challenging and supportive. Sign up for a FREE placement class at one of our local teaching centers, or explore our online courses for secondary school students at elementsofmathematics.com and eimacs.com. Like IMACS on Facebook for the latest information about our local classes and online courses.
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Every Career Field Needs People Who Are Good At Math


June 12, 2014 Filed under: Careers,Math Enrichment IMACS Staff Writer @ 1:00 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.

If you’re not planning on pursuing a so-called STEM career, do you really need to be good at math? Yes, but not just for the often-stated reason that people encounter math regularly throughout their lives. Being able to handle everyday math is certainly important. For example: If you’ve been offered varying aid packages by different universities, which one makes the most financial sense for your family? If you’re deciding between leasing or buying a car, which is the best deal in the long run? While no one doubts that being better at money arithmetic would benefit individuals and society as a whole, such specific situations require a narrow skill set.

The benefits of being good at math, however, go beyond correctly computing the tip at dinner to a wide array of circumstances that call for abilities prized in virtually every field of employment. For example, people who have learned to think mathematically are better at understanding the structure required to complete a given task. The first step in solving any math problem is sizing up the situation. What do you already know? What information is missing? Can you break the larger problem into more manageable pieces? Having both the skills and confidence to dissect complex problems, including ones that look nothing like what you’ve seen before, is one of the main benefits of becoming good at math.

People who have learned to think mathematically are also better at assimilating new ideas. Once you’ve assessed the situation, broken down the problem, and gathered the necessary pieces, how do you put it all together to get from where you are to where you want to be? When faced with a novel situation, can you devise an approach where there wasn’t one before? If you’ve studied mathematics in a way that pushes you to think both logically and creatively, then you will be much better prepared to handle an ever-changing variety of circumstances that call for these skills, no matter what career you choose.

Learn to think mathematically with logic and creativity at IMACS! Sign up for a FREE placement class at one of our local teaching centers, or explore our online courses for secondary school students at elementsofmathematics.com and eimacs.com. Like IMACS on Facebook for the latest information about our local classes and online courses.
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College Checklist: What Really Matters


May 15, 2014 Filed under: Gifted And Talented,Parenting IMACS Staff Writer @ 1:00 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.

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.

At IMACS, bright children reach their highest potential in math, computer science and logical reasoning by being appropriately challenged and supported. Sign up for a FREE placement class at one of our local teaching centers, or explore our online courses for secondary school students at elementsofmathematics.com and eimacs.com. Like IMACS on Facebook for the latest information about our local classes and online courses.
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What Does It Mean to be Genuinely
Good at Math?


April 17, 2014 Filed under: Critical Thinking,Logical Reasoning IMACS Staff Writer @ 8:35 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.

Have you seen the latest video of a young child reciting multiplication tables or the digits of pi? Or maybe you know a kid who has always gotten straight A’s. Pretty neat, but does it equate to being genuinely good at math? No. Bright students often do well in school with little or no effort. And an airtight memory facilitates excellent grades, especially when those grades depend on regurgitating information that’s already been provided. Being genuinely good at math is more about having a deep understanding of how and why things work. It also means being able to take that understanding and apply it in novel situations. This is where the ability to reason logically and abstractly separates skilled thinkers from those who only learned how to go through the motions. As IMACS graduate Zachary Kaufman put it, “College was so much easier with the logical thinking skills I learned at IMACS. While classmates tried to memorize each type of problem, I was able to strongly grasp core concepts and use them to solve any problem, even if it was different from those I had seen.” Zachary is a skilled thinker who is genuinely good at math. Will your child be?

IMACS specializes in helping talented children become skilled thinkers who are genuinely good at math. Sign up for a FREE placement class at one of our local teaching centers, or explore our online courses for secondary school students at www.eimacs.com and www.elementsofmathematics.com. Like IMACS on Facebook for the latest information about our local classes and online courses.
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From Public School to the Ivy League


March 20, 2014 Filed under: Parenting IMACS Staff Writer @ 1:00 am

The following excerpt is from the new book by Mandee Heller Adler, From Public School to the Ivy League: How to get into a top school without top dollar resources, which is available at Amazon.com. Ms. Adler is the founder and principal of International College Counselors, a Florida-based firm that provides expert strategies for admission to undergraduate colleges, graduate programs, business schools, law schools, medical schools, dental schools and other postgraduate schools.

From Chapter 4: Writing Essays …

ANSWERING THE QUIRKY QUESTIONS
In recent years, a number of colleges have been adding quirky questions to their applications. These supplemental questions are considered a way to get students to stand out from the crowd.

These questions have included:

  • Imagine you have to wear a costume for a year of your life. What would you pick and why?
  • What is your favorite ride at the amusement park? How does this reflect your approach to life?
  • What does Play-Doh have to do with Plato?
  • What would you do with a free afternoon tomorrow?
  • What was your favorite thing about last Tuesday?
  • The Spanish poet Antonio Machado wrote, “Between living and dreaming there is a third thing. Guess it.” Give us your guess.
  • According to Henry David Thoreau, “One is not born into the world to do everything, but to do something.” What is your something?

What colleges are looking for is your voice. Use this as an opportunity to demonstrate your “out-of-the-box” thinking. However, don’t go overboard. Admissions officers are looking to see if you’ll be an interesting person to have on campus. Interesting means imaginative, not crazy and not dangerous sounding.

GREAT FIRST SENTENCES
You need a great hook and a great first sentence. Opening sentences have the power to compel and fascinate. Some of our favorite student first sentences include:

  • For eight years, I have celebrated polyester.
  • I vividly recall coming home from school one day in Buenos Aires, Argentina, to find my house in disarray and my parents packing one suitcase after another.
  • I’ll admit it: I have a thing for gavels—a thing for motions and seconds and the clarity that they bring to meetings.
  • I eagerly reached into my Hello Kitty backpack.
  • Max prances in place as we await our turn into the arena.
  • Drip. Drip. Drip. Tick. Tick. Tick. As I lie in the hospital, waiting to be taken into surgery, I can only think that my IV drip sounds just like a metronome.

You want to read more, right?

FATAL ESSAY ERRORS
Application essays have been requested as part of the college application for the past umpteen years. The admissions teams have seen a lot of “creativity.” Here are their least favorite types of essays:

  • Metaphor. Don’t compare yourself to a mango, a Ferris wheel, or any other objects.
  • Death. Don’t write about a person or pet’s death unless it truly affected your life and you can use it to exemplify growth—for example, if someone died of cancer and you made it your mission to raise money/awareness, or if a death during high school affected your grades and caused you to stumble, but then you regrouped to overcome.
  • Free verse essays, essays written as raps, limericks, etc. Don’t emphasize form over function.
  • “Meta” essays where you talk about writing an essay, about the process of writing an essay, or about essays themselves.

Additionally, you should avoid writing about the topics below unless you have something extraordinary to say:

  • A trip to Europe
  • Generic admiration for your mom or dad
  • The controversial rock star or movie star whom you idolize
  • Overcoming an injury and making an athletic comeback
  • Volunteering at a local community center
  • Building homes in Costa Rica with Habit for Humanity
  • Understanding the meaning of life from a fishing trip

Sorry, but thousands of students have beaten you to these topics and then beaten them to death. These are called “cliché essays” because the reader knows from the get-go just where you are going with it.

THE VIDEO COLLEGE ESSAY
A number of college admissions departments are formally accepting video college essays.

The first step for any student is to view recent videos and see what others have done. This will give you an idea of the range of possibilities.

When it comes to actually making your video, it’s important to be original but in a way that is comfortable for you. Do what works for you. Your main goal needs to be communicating your message.

  • Start by identifying the question and any directions.
  • Think about what you want to say.
  • Write a script that is clear on the message and ideas you want to get across.
  • Collect resources and props that you want to use in the video.
  • Record the video until it’s as perfect as possible. Some students record the video themselves using a tripod while speaking directly into the camera; others enlist the services of a friend or family member.
  • Review your video and collect feedback.
  • Edit, edit, edit, and re-record if necessary.
  • Get more feedback.
  • Edit and re-record until it’s as perfect as it can be. Make sure it fits the requested length and meets all specs before sending it in.

To get a head start on preparing for college admissions, order a copy of From Public School to the Ivy League: How to get into a top school without top dollar resources from Amazon.com.

Prepare yourself for the rigors of college with university-level courses in computer science and mathematical logic from IMACS. Like IMACS on Facebook for the latest information about our local classes and online courses.
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IMACS Math Academy for Broward County Middle School Students


February 20, 2014 Filed under: Math Enrichment IMACS Staff Writer @ 1:00 am

The IMACS Math Academy is an intensive one-week program for exceptional students currently attending middle school in Broward County, FL, USA.
The IMACS Math Academy is an intensive one-week program for exceptional
students currently attending middle school in Broward County, Florida.

Broward County, Florida students currently attending grades 6-8 are invited to apply to the IMACS Math Academy, an intensive one-week program designed to stimulate talented students’ interest in mathematics beyond the traditional classroom. There is no cost to attend the IMACS Math Academy!

There are two scheduled sessions. The first will be held March 24 – 28 during Spring Break. The second will be held June 23 – June 27 during Summer Break. Both sessions of the IMACS Math Academy will be held at IMACS Headquarters in Plantation, Florida.

To be considered for one of the two available sessions, students must first complete an online aptitude test by February 28, 2014. Up to 60 students who do well on the aptitude test will be invited to apply to the IMACS Math Academy.

Parents interested in the IMACS Math Academy should visit www.imacs.org/mathacademy.

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AP Computer Science … Updating


January 30, 2014 Filed under: AP Computer Science,Computer Programming,Curriculum Development IMACS Staff Writer @ 1:00 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.

Following a recent review of the AP Computer Science A course and exam, the College Board has decided to replace its case study requirement with a requirement to complete a minimum of 20 hours of hands-on lab experiences. This change, which will take effect for the 2014-2015 school year, is being implemented to more effectively support student learning of core concepts in computer science. IMACS continues to follow closely all communications from the College Board, as well as discussions within the APCS community, on the forthcoming changes and will act accordingly.

From the beginning, IMACS’s philosophy has been to emphasize computational thinking and mastery of foundational ideas in computer science. This approach is reflected in how our Curriculum Development Group has meticulously designed our CS courses and, more importantly, in the success our CS graduates find in college, graduate school and at top tech companies. As such, IMACS fully expects that our AP Computer Science: Java Programming course will continue to exceed, as it always has, all of the College Board’s requirements and remain College Board-approved.

GridWorld Case Study

Since the 2007-2008 school year, AP Computer Science A has used the GridWorld Case Study to reinforce lessons on object-oriented programming.* GridWorld provides Java code designed to simulate the behavior of objects (Rock, Flower, Bug and Critter) in a grid. Ground rules such as Rocks cannot move, Critters eat Flowers and Bugs move forward and turn 45 degrees if blocked are part of the initial set-up. Given these starting parameters, students then write additional code that extends these various classes of objects. A student’s understanding of computer science concepts in the context of the GridWorld code is then tested on the AP exam with one free-response question and a handful of multiple choice questions.

College Curriculum Study

In 2011, the College Board undertook a College Curriculum Study in which institutions of higher education were surveyed about the AP Computer Science A course case study.^ Of the 117 institutions that responded, 91% said they were not likely to change their credit/placement policy for AP CS A if questions on the case study were not included in the exam. About two-thirds of respondents rated the inclusion of a case study as not important or only somewhat important.


“Although case studies have important benefits, their size and complexity have constrained the AP CS program in adapting to new course content and pedagogy.”
AP CS A Exploration of a Change from GridWorld to Labs

Clearly, GridWorld is now past its prime. As the College Board noted on its website, the case study requirement in AP Computer Science A needed updating “to stay aligned with the most recent practices in the continually changing field of computer science.”

Labs, Labs, and More Labs

This March, the College Board plans to release details of three sample AP Computer Science A labs as examples of how the new lab experience requirement may be implemented. One expectation is that their shorter length will make the labs easier to integrate into the course curriculum throughout the school year. Teachers and curriculum developers will have the flexibility to include sample labs or other comparable labs at points they feel are most relevant and pedagogically effective. It is also expected that the sample labs will be more connected to real-world situations, perhaps increasing student interest in taking the course and studying computer science.

Most importantly, labs are expected to support student learning of fundamental ideas in computer science. Whereas the case study questions on the current exam are tied heavily to the context of the GridWorld code, the 2015 AP Computer Science A Exam will test a student’s understanding of core concepts that are reinforced by hands-on lab experience, not knowledge specific to any particular lab. As an educational institution that has always emphasized foundational concepts in CS over code manipulation skills in the programming language du jour, IMACS is pleased to see the College Board take this important step.

Learn how you can give your child an unfair advantage in computer science. To find an IMACS teaching center near you, visit www.imacs.org. Talented middle and high school students can take university-level computer science online through our eIMACS distance-learning division.


*For readers who may be unfamiliar with object-oriented programming, it’s an approach in which the programmer creates “objects” with specified attributes and behaviors as modular, reusable code.
^http://tinyurl.com/LabsAPAC2013

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Letters to a Young Math Teacher


January 2, 2014 Filed under: Math Enrichment,STEM Education IMACS Staff Writer @ 1:00 am

The following letter is extracted from the new book, Letters to a Young Math Teacher, by Gerald Rising and Ray Patenaude, which is available from Amazon.com and other sources. Gerry Rising is Distinguished Teaching Professor Emeritus at State University of New York at Buffalo where he co-founded the university’s Gifted Math Program for highly-qualified regional students in grades seven through twelve. Gerry Rising was for many years associated with IMACS activities and is a strong supporter of our work.


Letter Seventeen: A Bag of Tricks

Paul Rosenbloom enjoyed an international reputation as a senior mathematician when I joined his Minnemath Project at the University of Minnesota as his assistant director. His Elements of Mathematical Logic remains today a basic resource recognized worldwide to be of historical as well as academic significance.

In our very first conversation he told me that he considered teaching outside the classroom an important aspect of a mathematician’s life and he urged me to develop what he called “a bag of tricks” from which to draw math-related lessons for people of all ages. I would later see him draw from his own collection in a number of settings. He could captivate anyone from nursery school students to scientific colleagues and even senior political figures.

Within a month of that conversation I found myself seated on an airplane flying from Minneapolis to Denver. My seat partners were a bored nine-year-old and her mother. When the mother learned that I was a math teacher, she asked me if I would be willing to “show Marjorie some math.”

Fortunately, I had been reading David Silverman’s book, Your Move, and I had some pennies with me. I played a series of Nim games with Marjorie, finding her an interested opponent and a remarkably quick study.

Nim, for readers unfamiliar with the word, is German for “take” and in this context it applies to games with players taking one or more counters like coins from a collection following a given set of rules.

We started with One Pile Nim. I set out a line of pennies on Marjorie’s tray and explained the rules. We would take turns, at each turn removing one, two or three coins. The winner would be the player who could take the last penny or pennies.* When she quickly determined the strategy for playing, I suggested she challenge her mother. Her eyes lit up as she outplayed her mom.

Now she wanted more. I suggested the misère form of the game: same rules for play but this time the loser forced to take the last coin. Now I had her mother’s full attention as well, but again Marjorie, once she found the winning strategy, could outplay mom.

We went on to play the very simple Two Pile Nim game in which each player takes any number of coins from one of two piles with the winner taking the last coin, but then the less transparent game, Woolworth, which is isomorphic to Two Pile Nim. Woolworth is named for the five-and-ten-cent stores of the 1950s that have been reincarnated as today’s Dollar Stores. On a sheet of paper I drew the following diagram:

I placed nickels and dimes as shown in the figure. One player controls the coins on the left, the other the coins on the right. Players alternate moving either of their coins any number of squares to left or right but without joining or passing the opponent’s coins. The object of the game is to squeeze your opponent so that no moves remain.

By the time I showed Marjorie the connection between Two Pile Nim and Woolworth we were well on our descent into the Denver airport. I was rewarded for our hour together when Marjorie turned to her mother to tell her that she wanted to become a mathematician.

Where do you find lessons like these that require no background and yet are suitable to given age groups? I found mine from two sources: my reading of journals and books about mathematics and my observation of lessons taught by others. Appendix 2 lists a few of the many available book sources.

Now, because it is a good story, I will tell you about my use of a lesson copied from the remarkable teacher, Robert Wirtz.^

Late one school year when I was a math supervisor I was asked by a primary school teacher to demonstrate Stern blocks for her students. Stern blocks are inch cross-section blocks that come in lengths from one to ten inches. Cuisenaire rods are similar but with centimeter dimensions.

I took several sets of Stern blocks to this teacher’s classroom and showed the six-year-olds some of the relationships among them.

The students were excited by the opportunity to mix play with learning, and I was convinced that they were gaining from the lesson. I noticed, however, that their teacher was not happy with the children’s mix of play with learning. Several times she interrupted their activities to tell individuals to be quiet.

It was clear to me that the teacher was convinced that I wasn’t disciplining the children in the way she wished, so I suggested that I return the next day to teach another lesson. Despite her reservations about my conduct of this class, she jumped at the chance to have me return. It was clear that she was happy to pass responsibility for these irrepressible kids off onto anyone she could find.

I had seen Bob teach a lesson to a similar group and the next day followed his model. Before the class I had the teacher gather the students in front of the chalkboard. Saying nothing to them I drew a square on the board and within it marked two star shapes. What I had drawn looked like this:

I pointed to that little tail at the bottom of the figure and turned to the class, holding out the chalk.

Several hands waved and I offered the chalk to one of the wavers. The boy came up and carefully wrote a “2″ below the diagram.

That got us started. I drew similar diagrams with different shapes and the children quickly caught on, competing to write the numbers below the figures. Then I began to complicate the requests by erasing their numbers and connecting two figures like this:

No problem. A volunteer wrote “5″ below the boxes.

I continued in this fashion, soon replacing the boxes with numbers but using the same connecting segments. All of the children were eagerly participating, but not one word was said by me or by any of them.

After a half hour of this activity, I finally spoke up, calling the children’s attention to the fact that none of us had spoken until then. And I turned to their teacher to congratulate them on what we had accomplished.

Unfortunately, my lesson proved nothing to this young woman. Her response: “Yes, after you left yesterday I really scolded them for their behavior and you saw the result this morning.”

Even with the best of efforts, you cannot always win.

I have talked about these mathematical extras mostly in terms of their use outside of your classroom, but they can play a role in your classes as well. Here is an example described by Swedish math educator Barbro Grevholm:


One of the teachers worked with a smaller group of pupils that had difficulties with mathematics. It was Friday and the pupils were not concentrating. The teacher announced that if they worked well he would play a game with them for the final ten minutes. This motivated the pupils to pay attention to the lesson. When the teacher finally said that it was time for the game, the students were all alert and extremely concentrated. In the game the teacher threw a single die nine times and after each throw read the result aloud. The pupils drew on sheets of paper three by three grids and chose to put the die calls successively in any one of the nine squares. The winner was the one who, by adding up the resulting three three-digit numbers, produced to a sum closest to one thousand. The game was played several times and all students took part eagerly. There was almost complete silence during the game and everyone made the additions quickly. For some of the pupils obviously more calculations were made during those ten minutes than during the earlier part of the lesson.

Please take the examples I have used only as samples of my own and others’ collections of activities. You may or may not add them to your collection. What is important is that you accumulate such activities that work for you. They will serve you well.


Where Do You Find Such Activities

Sources of such activities are all around you. You just have to be alert to them and adapt them creatively.

Many such activities come from your reading. Mathematics and mathematics education journals describe topics and lessons that you can both enjoy and share with others. Of course, you should credit your source when you replicate such a lesson, but every writer I know would be delighted to know that his or her lesson was being duplicated.

The two best journal sources I know for such examples are the Mathematical Association of America’s Math Horizons and the British Mathematical Gazette.

Some non-standard texts are full of such lessons. Authors like Harold Jacobs and Sherman Stein are two who have gathered and present such useful topics. And some authors simply collect such presentations. Among these are Ian Stewart, Ross Honsberger and Howard Eves.

In a class by himself is Martin Gardner whose collections of such topics are unsurpassed. His range is amazing, covering everything from hexaflexagons to fractal music, almost all of them serving a perfect basis for well-planned demonstrations.

Even your daily newspaper can provide activities. Although many people are drawn to the Sudoku puzzles, I much prefer three other popular forms: Kakuro, KenKen and Numbrix. These puzzels are adaptable to students of all ages (I solve one or two each day) and can challenge them all. The simplest appearing is Marilyn vos Savant’s Numbrix. While this puzzle task is appropriate for primary grade students (all it involves is listing the integers from 1 to 81 in order in a 9×9 grid), individual Numbrix puzzles range widely in difficulty.

In addition to their intellectual challenge, there are two things about the Kakuro and KenKen puzzles that I find attractive: (1) they involve basic calculation facts that reinforce the solver’s skills and (2) they appear as free apps on mobile phones and tablets. This availability makes them perfect puzzles to introduce to fellow travelers.

* The strategies for playing these Nim games are included in Appendix 4. I encourage you to play the games before you look at those strategies.

^ Bob Wirtz and his wife adopted a number of children with severe learning problems and they developed math materials to teach them. With Mark Botel, then president of the International Reading Association, he gathered those materials into books for elementary school students. Sadly, they are difficult to find today for they include some very attractive activities.

Are you searching for inspired teachers who understand your bright and talented child? Look no further than IMACS! Distance learners in our university-level gifted math and computer science programs are each assigned a principal IMACS instructor who is available to answer questions. Like IMACS on Facebook to get FREE weekly logic puzzles.
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Driven to Abstraction: Strengthen Your Thinking Skills with Computer Science


December 5, 2013 Filed under: AP Computer Science,Computer Programming,STEM Education IMACS Staff Writer @ 1:00 am

After school, weekend and online programs in math and computer science for gifted children who enjoy fun, academic challenges.
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Abstract reasoning ability entered the national conversation this year as the Common Core State Standards in mathematics were broadly implemented in the United States. In particular, one of the eight Standards for Mathematical Practice is to “reason abstractly and quantitatively.” The so-called STEM subjects — science, technology, engineering and math — are well-known for emphasizing this skill. Given that STEM-related fields are where most high-skilled job growth is predicted, today’s students would do well to develop their ability to think abstractly.

So what is abstract reasoning, and why is it so important? Let’s break it down: To reason is to use logic in piecing together information, usually with the goal of forming an inference or conclusion. Abstract simply means that this process is a thought-based exercise of the mind as opposed to being based in concrete experience. For example, if you know that ice melts at temperatures above 32°F, you can reason abstractly that an ice cube placed on the counter of your room temperature kitchen will melt. You don’t have to take an actual ice cube out of your freezer and observe it for an hour to arrive at this conclusion.

Of the subjects that you could study in order to develop strong abstract reasoning skills, computer science is a natural and practical choice, as well as being a highly creative and exciting area in which to learn and work. The programming aspect of computer science is well-known and is one area where abstract thinking matters a great deal. Programming, after all, is the creation of a set of instructions that a computer can follow to perform a specific task. Such tasks typically involve the manipulation of digital information, decidedly not the kind of stuff you can grab hold of to see how it reacts in the tangible world.

Learning to program well involves developing the ability to think logically and abstractly so that you can anticipate how the computer will react to the instructions you give. Great programmers are actually capable of writing simple code without having to check it with a computer because they have the ability to analyze processes in their minds. If you cannot think abstractly, you may still be able to get your code to “work” with trial-and-error tinkering, but that approach lacks the robustness needed to solve meaningful problems that tend to be more complex.

The rich experience of learning computer science, however, is so much more than coding. When you study computer science, you engage in computational thinking, in which logic, abstraction and creativity come together to help solve intellectually interesting problems. As Professor Jeannette Wing of Carnegie Mellon University argues in her seminal article* on the topic, computational thinking is a skill set from which everyone would benefit no matter their career path.

Why so? Because when you study computer science, your mind learns to grapple with high-level questions such as: How can existing information be used to deduce further information that will help solve the problem? How should a complex system be designed in order to maximize simplicity and usability? How can a complex problem be broken down into smaller pieces that are easier to solve? Can a common approach be devised to efficiently handle similar problems?

If these questions seem like they would be applicable in a wide variety of fields, STEM and non-STEM, it’s because they are. In essence, when you study computer science you learn the valuable skill of thinking abstractly like a computer scientist even if you don’t plan on becoming one.

*Wing, Jeannette M. “Computational Thinking.” Communications of the ACM 49:3 (March 2006) 33-35.

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