Sixteen Habits that Facilitate a Growth Mindset

by Benjamin Hebebrand, Head of School, Quest Academy

I distinctly remember a parent at our school (Quest Academy, a school dedicated to meet the needs of gifted students) proclaiming that “my child may not necessarily be gifted, but rather the school is helping my child in becoming gifted.” Such a statement naturally reflects the notion that giftedness or intelligence is not necessarily a fixed trait. Clearly, the work of Carol Dweck, summarized in her book Mindset, has helped us understand that developing a healthy growth mindset may be the single most important attribute required to develop one’s talents – this growth mindset implies that one internalizes the belief that one can continuously improve one’s learning and understanding or that one can “grow” and “exercise” one’s own intelligence.

While a healthy growth mindset may indeed be the supreme habit of mind, there are several habits of mind that may not be attributable to being intelligent but instead major contributors to becoming intelligent (or behaving intelligently). In the chapter “In the Habit of Skillful Thinking” included in the Handbook of Gifted Education (edited by Nicholas Colangelo and Gary Davis), habits of mind are defined as dispositions that must be applied when thinking strategically and effectively in a context of problem-solving, decision making, or knowledge generation.

We would be wise to list five characteristics that define a habit of mind, as outlined by Arthur L. Costa in the Handbook:

• Valuing – “choosing to employ a pattern of intellectual behaviors rather than other, less productive patterns.”
• Having the inclination – “feeling the tendency toward employing a pattern of intellectual behaviors.”
• Being alert – “perceiving opportunities for, and appropriateness of employing a pattern of intellectual behaviors.
• Being capable – “possessing the basic thinking skills and capacities to carry through with the behaviors.
• Making a commitment – “reflecting on and constantly striving to improve performance of the pattern of intellectual behavior.”

Keeping those five characteristics in mind, let us review a list of 16 specific habits of mind, all of which transcend any one single academic domain and also are, according to Costa, “ageless developmental qualities.”

1. “Persisting when the solution to a problem is not readily available.” This requires a repertoire of alternative strategies for problem solving. This habit of mind is similar to gifted education theorist JosephRenzulli’s attribute of task commitment, which along with high ability and creativity comprise his three-ring conception of giftedness.
2. “Managing impulsivity.” Students who blurt the first answer out may at times be well served to reflect on several options. This habit may help one avoid a potentially frustrating trial-and-error approach.
3. “Listening to others with understanding and empathy.” This habit of mind is described by Stephen Covey in the widely popular The Seven Habits of Highly Effective People. Costa recommends that “paraphrasing another person’s ideas” or “detecting indicators of another person’s feelings or emotional states.” He believes that the habit of listening is the “least taught skill in school.” Research shows that “we spend 55 percent of our lives listening.”
4. “Thinking flexibly.” This habit requires a tolerance for confusion and ambiguity in addition to one’s willingness to change one’s mind when presented with additional data.
5. “Thinking about our own thinking: Metacognition.” In a nutshell, this habit presupposes that one knows one’s own limits – what do we know and what do we not know. Fostering metacognition would include the act of rehearsing mentally prior to a specific performance and monitoring during the performance.
6. “Striving for accuracy and precision.” This habit most certainly involves double-checking one’s work. I recall that as a teacher I never accepted a student’s test or in-class essay without challenging my students to double and triple check. I spent time instructing students how to double-check their work.
7. “Asking questions and posing problems.” This habit is a follow-up to the habit of metacognition as one needs to learn to ask the questions to learn and understand that what one does not know.
8. “Applying past knowledge to new situations.” This habit requires students to relate and apply previously learned material to new challenges.
9. “Thinking and communicating with clarity.” Underlying this habit is that “fuzzy language is a reflection of fuzzy thinking.”
10. “Gathering data through all senses.” This habit requires full attention to one’s environment and processing information coming to the brain via gustatory, olfactory, tactile, kinesthetic, auditory, and visual sensory pathways. Students with wide open sensory pathways will absorb more information than students who are “oblivious to sensory stimuli.”
11. “Creating, imagining, innovating.” Students are well served in problem solving when they “examine alternative possibilities from many angles.” Students who exemplify this habit are unlikely to accept the status quo, instead seeking greater novelty.
12. “Responding with wonderment and awe.” Joyful and energetic curiosity is a trait that defines this habit. This habit transcends the “Yes, I can” attitude, better characterized as “Yes, I enjoy.” I recently observed one of our math students assigning a problem that “will make your head hurt.” The advanced math students related to this challenge just as the math teacher intuitively had predicted – they were looking forward to the “brain teaser” problems.
13. “Taking responsible risks.” Students who “accept confusion, uncertainty, and the higher risks of failure” are likely to exemplify this habit.
14. “Finding humor.” This habit may best be exemplified by those students who “thrive on finding incongruity and perceiving absurdities, ironies, and satire.”
15. “Thinking interdependently.” There is a reason why all good classrooms include group projects, as in our technological age “no one person has access to all the data needed to make critical decisions; no one person can consider as many alternatives as several people can.” Habits such as listening, seeking consensus and foregoing one’s own ideas and work and instead accepting someone else’s are part of working and thinking interdependently.
16. “Remaining open to continuous learning.” This habit may best be described as keeping an open mind, “inviting the unknown, the creative, and the inspirational.”

In summary, teachers, parents, mentors, and coaches are wise to spend significant time in helping students develop these habits, in turn teaching them to “behave intelligently.” I would propose that a successful internalization of these 16 habits are all ingredients that facilitate a healthy growth mindset. 

System 2 Thinking: Is Critical Thinking Valued in Gifted Education?

When we use the terminology “critical thinking” in everyday language, we often associate this type of thinking with the notion of skepticism. The inquiry “Is this really true?” may be construed as a challenge, but actually I would prefer this most basic question be viewed as taking the time out to judge or evaluate any given statement, idea, solution or belief. Indeed, the term “critical” finds its roots in the Greek verb “krinein,” meaning to judge or evaluate. If we complement the term “critical” with “thinking,” we are now “adding the use of reason as the means of evaluation,” as Brenda Linn and Bruce M. Shore assert in their chapter of “Critical Thinking” in the aptly named “Critical Issues and Practices in Gifted Education,” published by the NationalAssociation of Gifted Children.

The process of thinking by itself may be close to spontaneous or instinctive as may be the behavior or act of making critical statements. Grouping these two terms together, however, it is easy to recognize that critical thinking is a rich process of thinking about validity or truth. The 2011 book Thinking, Fast and Slow  by Nobel Memorial Prize winner in Economics Daniel Kahneman indeed summarizes years of his and other research that there are two fundamental systems of thinking (and the book also hints at the notion that we generally place too much trust in human judgment).

These two systems of thinking are generally categorized as System 1 and System 2 thinking models. Critical thinking falls into System 2. Educational psychologist Keith E. Stanovich views “critical thinking as rule-based, conscious, relatively slow, serial, resource-intensive, controlled, decontextualized, and acquired by cultural transmission and formal learning.” He contrasts that with System 1 Thinking (or The Autonomous Set of Systems (TASS)) that “is relatively undemanding of cognitive capacity, relatively fast, and is acquired from biology, exposure, and personal experience.” Linn and Shore offer the further contrast of Systems 1 and 2 based on their research of other scientists who characterize System 1 as “an automatic, heuristic-based, tacit, gist, fuzzy trace, or holistic processing system,” and System 2 as “a systematic, rational, explicit, or analytical processing system.”

Linn and Shore state that popular culture views System 1 as the “intuitive, holistic, spontaneous, even reflexive – the locus of intelligence….capable of reacting in deeply unintelligent ways,” while System 2 is that thinking that enables us “to override the built-in biases of the older, more automatic System 1.” (Kahneman describes how System 1 Thinking lulls us into a sense of being tricked. He cites a simple algebraic problem – a baseball and a bat cost $1.10 combined, and the difference in price between the bat and the ball is one dollar. The overriding majority of quick responses as to the price for each item is $1 for the bat and ten cents for the ball, which obviously does not account for the condition that the bat is $1 higher in price than the ball).

There is little evidence of research as relates especially to the two-system model, which has focused on the field of gifted education, but yet Linn and Shore assert that “basic critical thinking research has direct implications for the teaching of gifted students.” The first such implication is best summarized by psychologist Robert Sternberg’s question of “why do intelligent people believe and do such foolish things,” and Stanovich’s reply of “what can be done about that?” Furthermore, Linn and Shore suggest that critical thinking skills are “not being taught in most school curricula, including those intended for highly able students.”

R. H. Ennis, originator of the Cornell Critical Thinking Test, asserts that often critical thinking is confused with problem-solving or higher order thinking. He identified what he called critical thinking dispositions -- "asking a question, asking for clarification, and acquiring relevant background information." He credits his colleague Lowell Hedges for putting forth specific abilities that should be fostered to become a critical thinker. They are: 

1.  The ability to identify and formulate problems, as well as the ability to solve them.
2.  The ability to recognize and use inductive reasoning, as well as the ability to solve them.
3.  The ability to draw reasonable conclusions from information found in various sources, whether written, spoken, tabular, or graphic, and to defend one’s conclusions rationally.
4.  The ability to comprehend, develop, and use concepts and generalizations.
5.  The ability to distinguish between fact and opinion.

Linn’s and Shore’s chapter in the Gifted Education Handbook conclude that “gifted students enjoy learning about tricky tasks, deceptive arguments, and misleading kinds of arguments more than students who are less able to think abstractly and meta-cognitively. Less enjoyable for gifted students may be the process of critically analyzing their own thinking dispositions.” Interestingly enough, the authors believe that this lesser enthusiasm is the result of our methods by which we identify gifted students. “The ability to arrive at the expected answer, rather than to wrestle with problems and formulate objective and defensible solutions, may have dominated the process by which their giftedness was identified.”

Broadening the View on Intelligence: Multiple Intelligences

by Benjamin Hebebrand, Head of School, Quest Academy

The method by which we initially began to measure intelligence has led to what some scholars call a “narrow view of intelligence” – a view that is tied closely to the skills that we value the most in school: ‘linguistic and logical-mathematical skill,” according to 2003 edition of The Handbook of Gifted Education, compiled by Nicholas Colangelo and Gary A Davis.

This school-based view of intelligence can be traced back all the way to the beginning of the 20^th century when Alfred Binet initially began devising measurements “that could assist in identifying students who were likely to fail in elementary school.” Binet’s work was the basis to Lewis Terman’s development of the Stanford-Binet Intelligence Scale in 1916.

In the Handbook of Gifted Education, several authors, including Howard Gardner, who in 1983 broadened the traditional school-based view of intelligence by putting forth his Multiple Intelligences (MI) theory, insist that “a high IQ score remains the most common standard for admission to specialized programs for the gifted and talented.”

But it clearly is Gardner’s work that has broadened our view of intelligence, even if it has not yet led to a shift in admission practices to gifted education programs. By incorporating a MI approach to conceiving and measuring giftedness, gifted education may not only reach “students who are gifted in the traditional sense of the word,” but also “students who are gifted in one or more culturally valued areas.” Additionally, proponents of MI would argue that a “MI perspective can enhance (gifted students’) understanding through application of multiple entry points.” Conversely, a traditionalist point of view toward intelligence may espouse the notion that looking beyond linguistic and logical-mathematical dilutes the academic experience in a gifted education classroom.

Essentially, Gardner’s work “threw into question the idea that an individual’s intellectual capacities can be captured in a single measure of intelligence.” Instead, Gardner defines intelligence as a “biopsychological potential to process information in certain ways: Each intelligence can be activated in an appropriate cultural setting.” While Gardner’s MI theory puts intelligence in a more universal context, it also opens the door to the idea that there may be culturally different interpretations of intelligence – possibly an idea that relates to cultural relativism. By employing a MI point of view, we “permit an individual to solve problems and fashion products that are of value within a cultural context,” according to Gardner, Catya vonKarolyi, and Valerie Ramos-Ford, as cited in their entry entitled “Multiple Intelligences: A Perspective on Giftedness,” included in the Handbook of Gifted Education.

Initially, Gardner put forth seven intelligences in his publication entitled Frames of Mind, which have recently been updated to include nine different intelligences. They are summarized in the Handbook by “core operations” as follows:

·         Linguistic: “Comprehension and expression of written and oral language, syntax, semantics, pragmatics.” William Shakespeare is cited as an example.

·         Logical-Mathematical: “Computation, deductive reasoning, inductive reasoning.” Example: Isaac Newton

·         Musical: “Pitch, melody, rhythm, texture, timbre, musical, themes, harmony. Example: Wolfgang Amadeus Mozart

·         Spatial: “Design, color, form, perspective, balance, contrast, match.” Example: Frank Lloyd Wright

·         Bodily-Kinesthetic: “Control and coordination, stamina, balance, locating self or objects in space.” Example: Tiger Woods

·         Interpersonal: “Ability to inspire, instruct, or lead others and respond to their actions, emotions, motivations, opinions, and situations.” Example: Dalai Lama

·         Intrapersonal: “Knowledge and understanding of one’s strengths and weaknesses, styles, emotions, motivations, self-orientation. Example: Oprah Winfrey

·         Naturalist (added later): Noting the differences that are key to discriminating among several categories or species of objects in the natural world. Example: Charles Darwin

·         Existential (unconfirmed ninth intelligence): Capacity to raise big questions about one’s place in the cosmos. Example: Soren Kierkegaard

While MI theory states that “each intelligence is a relatively autonomous intellectual potential capable of functioning independently of the other,” it also puts forth the idea that the different “intelligences work in concert with each other.” While MI certainly defines intelligences in a more universal manner, it cautions also to suggest that there are individuals who are universally intelligent, i.e. possessing high degrees of ability or talent in each of the nine intelligences. Gardner references a “jagged profile of abilities.”

“It cannot be assumed that an individual who demonstrates exceptional linguistic and logical-mathematical skills – abilities tapped by IQ tests – will also display exceptional ability (or even interest) in activities relying on interpersonal or kinesthetic intelligence, for example. Neither can it be assumed that a child who performs poorly on an IQ test or standardized achievement test will fail to excel in activities relying on one or more of the other intelligences,” according to the Handbook.

Talent Search programs offer gifted students additional norm reference points

by Benjamin Hebebrand, Head of School, Quest Academy

When young children consistently score at the 95^th %ile or higher level on in-grade standardized tests (tests that measure at the grade level in which the test taker is enrolled), they and their parents may well be served to test beyond the grade-level standardized testing that is offered at schools. Adaptive tests (technology-based exams by which the level of complexity adjusts according to the answers keyed in by the students) such as Measures of Academic Progress (MAP) practically remove the ceilings of in-grade or at-grade-level standardized tests. Thus, students and parents can generally determine the grade-level at which the child is achieving – and maybe more importantly, teachers can differentiate their instruction.

But parents attempting to glean a better picture of how their child is faring vis-a-vis other students who also excel at in-grade testing have turned to annual university-based Talent Search competitions. More than 300,000 students participate annually in Talent Search competitions such as the Midwest Academic Talent Search offered by Northwestern University’s Center for Talent Development.

Talent Search research shows that “when students in the upper tail of the typical normal curve take a test designed for older students, a new bell curve results,” according to the Handbook of Gifted Education compiled by Nicholas Colangelo and Gary A. Davis. “Administering an above-level test to students at the upper end of a bell curve helps discriminate able students from exceptionally able students, and it provides a more precise assessment of aptitude and readiness for additional academic challenges.”

Most assessments used by the various Talent Searches (other than Northwestern University, there are numerous other such programs affiliated with universities such as Johns Hopkins University, Duke University, Carnegie-Mellon University, University of Denver to name a few) employ tests that were developed for “students two to four years older than the students’ present grade placement.”

The test most commonly used test in the Talent Search movement is the SAT, typically administered to students at the 7^th and 8^th grade levels. The SAT, of course, is in addition to the ACT this country’s major college entrance examination typically administered to high school juniors and seniors. Julian Stanley, credited with initiating the Talent Search movement in the 1970s with his well-known Study of Mathematically Precocious Youth (SMPY) found in his research that the math section of the SAT exam “must function far more at an analytic reasoning level for Talent Search participants than it does for high school juniors and seniors.”

Talent Search SAT results allow test takers to receive normative data on two different levels – a) compared to the nationwide results achieved by high school juniors and seniors; and b) compared to all Talent Search participants.

As concerns the comparison to SAT nationwide results achieved at 11^th and 12^th grade levels, SAT verbal testing data obtained by John Hopkins University in 2001 for its Talent Search participants, for example, show that 22 percent of 7^th grade males and 45 percent of 8^th grade males did as well or better than the 507 score recorded at the 50^th percentile level for high school juniors and seniors. The numbers for female participants are 24 percent at the 7^th grade level and 47 percent at the 8^th grade level. That same year, the study showed on the mathematics section that 59 percent of 8^th grade female participants surpassed the mean score for female high school juniors and seniors.

As concerns the comparison of Talent Search participants, Northwestern University’s Center for Talent Development Director PaulaOlszewski-Kubilius offers this scenario: “Take, for example, two seventh grade students who both score at the 97th percentile on the mathematics composite of their in-grade achievement test. When they take the SAT-Math, however, one student scores a 550 and the other a 350. These students look very similar to one another on the basis of the in-grade achievement test and would be treated similarly educationally by schools and teachers. In reality, they are quite different and need different educational placements and programs.”

Talent Search programs also test students younger than the 7^th and 8^th grade students typically offered the SAT or also the ACT. Students as early as third grade are offered above-grade level testing. Northwestern University’s Midwest Academic Talent Search (NUMATS) offers students at that age the EXPLORE testing, developed by ACT to test 8^th grade students.

Our school, Quest Academy, offers 6^th through 8^th grade students the EXPLORE testing in addition to conducting MAP testing at 1^st through 8^th grade levels. In addition, the school encourages its gifted students to participate in NUMATS. Interestingly enough, the Illinois Math and Science Academy (IMSA), the state-funded boarding school for gifted students throughout Illinois, requires applicants to submit SAT testing data. Analysis of accepted IMSA students in the year of 2010 (including Quest Academy students) show that 8^th grade students achieved a SAT math score of 732 and a Critical Reading Score of 671.

Social Development of Gifted Children

by Benjamin Hebebrand, Head of School, Quest Academy

It is mostly due to common stereotypes that gifted children are occasionally (and I would add unfortunately) portrayed as “geeky,” “quirky,” or somehow inept at forging and maintaining meaningful friendships or other types of relationships. The research actually tells a different story. According to Nancy M. Robinson, professor emerita at the University of Washington and author of Social and Emotional Development of Gifted Children “gifted youngsters, as a group, are probably more robust than an unselected group of their agemates” when investigating social vulnerabilities. “But neither are they (gifted youngsters) immune to the social-emotional issues and disorders that other people endure.”

Because gifted students possess unique intellectual characteristics, it is rather likely that these characteristics have a direct impact on personality traits that gifted students develop. In essence, one’s thinking influences one’s way of presenting oneself or being perceived in social situations. Linda K. Silverman, director of the Institute for the Study of Advanced Development, as well as the Gifted Development Center in Denver, Colorado, presents how some gifted intellectual traits may translate into personality traits. These traits, in my opinion, can lead to both positive and negative consequences in social contexts:

1)     Exceptional reasoning ability may lead to insightfulness: this may indicate that gifted youngsters develop a grasp on social dynamics.

2)     Intellectual curiosity may lead to gifted child’s need to understand: this may indicate that a gifted child asks many questions about social contexts.

3)     Rapid learning rate may lead to a gifted child’s need for mental stimulation: this may lead to behaviors in social contexts where a child is perceived to be tuning out or to advance a social interaction with meaningful comments or observations.

4)     A vivid imagination may result in an excellent sense of humor: this may lead to a gifted child’s tendency to find and bring about humorous associations in social contexts. Sometimes, the humor is too imagination-rich for others to follow.

5)     A passion for learning may lead to intensity: this may cause a gifted child to dwell on certain moments or statements occurring in social situations.

A 2002 task force commissioned by the National Association for Gifted Children confirmed Robinson’s findings by concluding that “high ability students are typically at least as well adjusted as any other group of youngsters.” Interestingly enough, the task force also determined that gifted children face situations that may present challenges and risks to their social-emotional development. The following were identified:

1)     Gifted students’ intellectual and social advancement as compared to age peers may result in “social environments poorly calibrated to their interests, language, and personal maturity.

2)     School settings that do not match “the level and pace of their learning and understanding.”

3)     Gifted students may be prone to asynchronies or uneven internal developments (i.e in a rather general sense a child’s cognitive development may be far more advanced than one’s social-emotional development).

4)     Gifted students may experience higher “tensions” due to their “creativity, energy, intensity, and high aspirations, often far greater than those expected at their age.”

5)     Gifted children may also wish to be “like everyone else” and thus are tempted to “deny their abilities in the service of finding friends.”

6)     Sadly, gifted students may encounter milieus that do not value intellectual traits (anti-intellectual). Such environments may be unfriendly and negative toward the gifted child.

Research has uncovered various coping skills that gifted pre-adolescents and early teenagers (ages 11-15) report in terms of dealing with challenges and risks posed by their intellectual giftedness and associated personality traits. Thom Buescher, who works with gifted adolescents, has recorded several behaviors and mindsets that gifted adolescents have reported to him – these coping skills are listed in order of preferred choices. This implies that some coping skills are better than others – the ones listed toward the bottom of this list are not recommended, while the ones on top are indeed good choices:

1)      “Become comfortable with your abilities and use them to help peers.”

2)      “Seek friends among other students who have exceptional abilities.”

3)      “Select programs and classes that are designed for gifted students.”

4)      “Seek adults to relate to.”

5)      “Focus on achieving at school in nonacademic ways.”

6)      “Develop talents outside of school.”

7)      “Engage in community activities where age is unimportant.”

8)      “Avoid programs designed for gifted students.”

9)      “Change language and behavior to mask your true abilities.”

10)   “Acting like a ‘brain’ so friends leave you alone.”

11)   “Pretending to know less than you do.”

At a gifted education school such as Quest Academy, where I serve as Head of School, we have chosen to meet the academic needs of children in a nurturing environment. As a result, we have adopted a school-wide character education system that not only facilitates appropriate behaviors in social contexts, but also performance character, whereby gifted students can properly reflect on their intellectual gifts in developing a sense of modesty, industry, patience, and self-discipline.

THINKING: Cogito Ergo Sum

By Benjamin Hebebrand, Head of School, Quest Academy

Most – if not all of us – have encountered classrooms with posters encouraging us to THINK or we may also have encountered teachers who would use expressions such as “THINK before you answer.” I was lucky to have a teacher who encouraged me to think meta-cognitively by proclaiming “THINK about how you THINK.”
 

“In teaching for thinking, the concern is not how many answers students know, but what they do when they do not know; the goal is not merely to reproduce knowledge, but to create knowledge and grow in cognitive abilities,” according to “Best Practices in Gifted Education” a 2007 publication released by the National Association for Gifted Children.
 

Improving our students’ thinking most certainly is a goal in general education, but the field of gifted education has specifically researched thinking styles attributed to gifted children and how best to foster or teach thinking skills to gifted children.
 

B. M. Shore and L.S. Kanevsky in a 1993 article identified seven possible differences or attributes as relates to cognition by gifted children. They are:

·         Gifted children may be able to draw upon more existing knowledge and use this knowledge more effectively

·         Gifted children more often and more efficiently engage in metacognitive processes

·         Gifted children give the cognitively complex parts of problem solving a greater commitment of time, allowing them to solve and report problems

·         Gifted children show greater understanding of problems especially in terms of commonalities and transfer (Personally, I will add here that as a bilingual person, I find my thinking has greatly benefitted by analyzing the similarities and differences between my native language of German and my second language of English)

·         Gifted children utilize assumptions that they will investigate systematically

·         Gifted children show greater flexibility in choosing strategies and points of view

·         Gifted children are intrigued joyfully and creatively when presented with complexity and challenge in their tasks
 

Over the years, the identification of gifted children has given cognition greater emphasis. In 1993, R. J. Sternberg and E.L. Grigorenki contributed to this process by dividing thinking into three general areas, best illustrated by what they termed “mental self-government.”

·         Legislative function: This type of thinking involves the idea of creating, imagining, and planning

·         Executive function: This type of thinking facilitates implementation

·         Judicial function: This type of thinking incorporates all thinking related to the process of evaluating
 

As far as fostering or nurturing a child’s thinking processes, teachers may well be served that thinking can indeed be taught and practiced. Particularly in the field of gifted education, but also in general education, we have come to employ the idea of “higher order (or level) thinking.” As teachers, we want our students to spend less time and work at the knowledge and comprehension levels but rather in the higher order thinking modes that Bloom’s taxonomy identifies with levels such as “application (of knowledge), analysis, synthesis, and evaluation.”
 

More specifically, The NAGC Handbook of “Best Practices” outlines several broad categories to be included in daily instruction to help foster a child’s thinking: They are a) critical thinking; b) creative thinking; c) problem finding; d) metacognition; e) domain-specific (i.e. mathematics) patterns and forward thinking; f) correlational thinking; g) reflective inquiry; h) questioning created for memory, divergence, convergence, aesthetics, and ethics; i) inquiry and investigation; j) dialectical thinking skills; and k) Socratic discussion.
 

In their 2005 publication entitled “Being gifted in school: An introduction to development, guidance, and teaching.” L.J. Coleman and T.L. Cross conclude that an “overwhelming majority of teaching methods reported in the literature on gifted education are variations on creativity, problem-solving themes. Their major characteristics involve suspension of judgment, practice in generating responses, and opportunities for children to consider how they think.”
 

At our gifted education school, Quest Academy in Palatine, Illinois, we have for more than a decade designed our curriculum not primarily around knowledge and comprehension, but rather conceptual understandings to which we refer as Enduring Understandings. It is within those higher-level understandings that we then also spend instructional time on specific academic knowledge and comprehension. 

Defining Mathematical Giftedness in Elementary School Settings

by Ben Hebebrand, Head of School, Quest Academy

The field of elementary school mathematics tends to be viewed as a sequential advancement of specific mathematical skills, occasionally resulting in a mindset that young students can accelerate their mathematical learning by “racing” or “flying” through checklists of specific mathematical skills. Indeed, I occasionally hear gifted education colleagues describing elementary mathematics as an “arms race” mentality, in which the checking off of specific sequential math skills such as single-digit or double-digit addition become the sole focus of math learning.

Mathematics is indeed an undertaking far more than a simple progression of mathematic skills and operations. The definition of mathematical giftedness may indeed help us pinpoint what we believe to be essential in developing mathematical talent.

Surprisingly, there has been “little research conducted on what constitutes mathematical giftedness,” according to M. Katherine Gavin and Jill L. Adelson, authors of a chapter entitled “Mathematics, Elementary,” published in the comprehensive gifted education handbook “Critical Issues and Practices in Gifted Education.” Most of the research focuses on the traits that mathematically gifted children display.

In the late 1960s and most of the 70s, Russian psychologist V. A. Kruteskii in a Piaget-like manner observed students, aged between 6 and 16, whom he labeled “not capable,” “capable,” and “very capable.” His research has been divided into the four major giftedness categories of “flexibility, curtailment, logical thought, and formalization:

• Flexibility: Students switch strategies in solving a problem with ease and numerous times to help them make sense of the problem.
• Curtailment: Students skip several steps in the logical thought process because they see the solution as one whole thought as opposed to linearly connected logical steps. This phenomenon may help us understand why some gifted math students cannot explain their reasoning in finding a solution as they just cannot retrace any step-by-step process that are required for less capable math students.
• Logical Thought: These are students who think in mathematical symbols such as “less/greater than” or “plus/minus” when filtering data that is being presented to them. These thinkers “look at the world from a logical perspective.”
• Formalization: Based on just very few examples, students can see the overall structure of a problem and thus make generalizations very quickly.

Agreeing on a universal definition of mathematical giftedness is further compounded by the sub-sets of algebra and geometry. Kruteskii spoke of students with an “algebraic cast of mind,” characterized by very abstract thinking, while “geometric” minds tend to visualize problems pictorially. Kruteskii actually observed that especially elementary-age students who displayed both minds, culminating in what he termed a “harmonic” mind, are highly capable mathematicians. One final important observation that Kruteskii contributed toward the idea of defining giftedness roots in attributes that actually are not “obligatory.” Specifically, he singled out “swiftness, computational ability, and memory for formulas and other details” as characteristics that do not necessarily contribute to mathematical giftedness.

J.E. Davidson and R.J. Sternberg in a 1984 edition of Gifted Child Quarterly article entitled “The Role of Insight in Intellectual Giftedness, reported on work with fourth through sixth grade students that mathematically gifted students use three progressive “insight” processes:

• Selective encoding: These students can “sift out” relevant information from a problem situation.
• Selective combination: These students synthesize the relevant information.
• Selective comparison: Students compared the information that had been synthesized together to other relevant information.

While speed is highly valued in mathematical competitions such as the “Final Round” in a MATHCOUNTS contest, it is important to note that Davidson and Sternberg pointed out that ”speed in doing mathematics is important but is secondary to insight.” The remaining research in identifying characteristics of gifted math students points toward math students’ “focus on conceptual understandings,” “ability to abstract and generalize,” and “persistence and ability to make decisions in problem-solving situations.”

In making the leap from defining mathematical giftedness to identifying mathematical giftedness, the practitioners of gifted education frequently – if not solely – rely on norm-referenced standardized intelligence, aptitude, and achievement tests. It is particularly the use of standardized achievement tests that is questionable, as those tests tend to focus on “low-level tasks that require students not to think and reason in ways that Kruteskii observed as defining attributes of mathematical giftedness,” as research by L.J. Sheffield of the National Research Center on Gifted and Talented points out. According to this research, the vast majority (up to 62 to 82% of the items) of questions dealt with the topic of number and operations, of which the clear majority focused on computation. The most common method in identifying mathematical giftedness is the practice of using out-of-level tests such as SSAT-L, PLUS, or EXPLORE (the test that both Quest Academy and the Center for Talent Development at Northwestern University employ). There is research that suggests these tests eliminate the ceiling effect (students reaching the highest level of their mathematical ability) for 98 percent of the students.

STEM is Gifted Education

by Benjamin Hebebrand, Head of School, Quest Academy

Education in Science, Technology, Engineering, and Math, nowadays referred to as STEM, has risen to the forefront as a result of poor performance by U.S. students on international testing in addition to an ever-increasing need to innovate to remain competitive in a global economy that is migrating toward ever-increasing levels of automation. A closer look at best practices in gifted science education shows that our field has for a long time embraced the idea of exploratory STEM education.
 

Exemplary instruction in these subjects, particularly science, centers on a hands-on approach. The National Research Council in 1996 simply stated that “learning science is something that students do, not something that is done to them.”
 

The hands-on approach is absolutely congruent with research that identifies personality traits of scientists. This research cites qualities such as “risk-taking, autonomous, unconventional, original, persistent, attentive toward unusual details, independent, playful, disliking ambiguity, interested in art/humanities, curious, intellectually courageous, and daring.”
 

Such qualities do not lend themselves well to traditional science instruction that first places emphasis on “knowledge of facts, laws, theories, and applications.” This emphasis has been so heavily imprinted that the actual playful part of science – the laboratory exercises or activities – has served the purpose of verification.
 

Simply completing labs as a means to verify book-learned concepts and facts is not conducive to shaping scientists to whom we essentially entrust the notion of problem-solving. Nor does the idea of verification conjure up images of innovation.
 

The field of gifted education long ago has identified problem-solving as a necessary component of high quality science instruction particularly aimed at gifted students. Robert Sternberg already in 1982 wrote in a Roeper Review article entitled “Teaching Scientific Thinking to Gifted Students” that gifted science education should emulate what scientists do and therefore should focus on “a) problem-finding; b) problem-solving; c) problem re-evaluation, and d) reporting.” The idea to allow students to identify a scientific problem rather than being assigned such a problem is nowadays a central idea in STEM education – quite frankly an idea that has always been part of science project learning (i.e. high quality science fairs) that is commonly found in gifted education. Sternberg views problem-solving as “problem identification, selection of the process for solving, solution monitoring, responding to feedback, and implementing an action plan,” whereby re-evaluation “requires analyzing the outcomes that may be expected or unintended.” Clearly, Sternberg views science instruction as a process that is capped by reporting – the action that “clarifies thinking and is an integral part of the scientific process.”
 

STEM education seeks to employ a design process to enhance the problem-solving component. By incorporating technology and engineering, students will design and engineer practical solutions to scientific problems. The Teaching Institute for Excellence in STEM outlines similar process skills as Sternberg’s. The components are 1) Identify the Need or Problem; 2) Research the Need or Problem; 3) Develop Possible Solutions; 4) Select the Best Possible Solutions; 5) Construct a Prototype; 6) Test and Evaluate the Solution(s); 7) Communicate the Solution(s); and 8) Re-design.
 

The added design element in STEM education clearly invokes the idea of creativity. Design not only is about function, but also form. As such, STEM nowadays has added the A for Art to form STEAM. The interdisciplinary nature of STEAM also is a long-held practice in gifted education – enhancing the learning experience in multi-faceted domains.

Parenting Gifted Children

By Benjamin Hebebrand, QuestAcademy 

The transformation of a child’s giftedness into talents or abilities is impacted by a multitude of factors and persons. Fully or optimally developing potential is among the most researched and discussed topics in both the soft and hard sciences. Theories abound across cultures and across disciplines such as psychology, neuroscience, or biology. Central in all developmental theories is the role of parenting – and while parenting is not a science, it is a topic that is much debated and critiqued and researched and tracked – and within that research is limited thought given to the idea of parenting gifted children.  

The most important realization – particularly for first-time parents – is to recognize and accept that there is no “magic” or “scientifically prescribed” approach to parenting gifted children. “The only conclusion to be drawn from studies to date is that there is not one superior type of parenting, nor one set of identifiable set of family dynamics that leads to the fulfillment of a child’s potential,” according to Robin Schader, research professor at the Neag Center for Gifted Education and Talent Development at the University of Connecticut. This obviously underscores the beauty and mystery of individual differences among gifted children and their parents. As such, it is best to value both the child’s and parent’s individuality. In recent years, we have been bombarded with literature about parenting with an eye toward talent development. In my mind, two central themes have crystallized themselves in recent years – maybe these are the new “folk wisdoms” in parenting gifted children – 1) that excessive praising or rewarding a child’s achievements may actually result in thwarting a child’s potential; and 2) that actual hard work and practice is required to transform giftedness into talents and that engaging in and completing such work is most rewarding to the child (it is the “intrinsic” reward). 

But yet of course it is only natural or human for parents, particularly first-time parents, to seek information about parenting, particularly when parenting involves a child who displays giftedness traits that may not be observable in other children – and thus, makes one’s child different from other children. Such differences manifested by giftedness are not what make kids superior or inferior but rather have the potential to influence a child’s life in terms of his or her learning both on cognitive and social-emotional levels. At this point, it may be evident that a gifted child may thus have needs that are different from those of many children. 

As parents, we all want to do the best in meeting those needs. A review of thousands of parental inquiries received at the National Association for Gifted Children reveals that a little more than a third of questions revolved around the theme of how to recognize giftedness and how to enrich a gifted child. “My child is different than others her age. How can I find out if she’s gifted,” or “How can I help my child develop his exceptional abilities and assure they don’t go to waste,” is how Schader summarizes these questions. A little more than a quarter of inquiries seek information on programs or specific schools for gifted children. Thus, we can conclude that among the earliest parental decisions to be made in a young gifted child’s life is to 1) have the child assessed and confirm giftedness (please see a previous blog entry entitled “Early Identification of Giftedness”); and 2) to offer the child an educational experience that is different than what can be found in most schools. 

It is my experience that if parents have successfully undertaken these first two steps of identifying the level of giftedness and selecting an appropriate school that a child’s achievement record becomes less of an issue. Conversely, if a child’s giftedness has gone undetected and no specific gifted education programming options have been offered, a gifted child may experience learning issues such as boredom or underachievement.  

Of course, when we discuss parenting and its influence on developing potential, we often wonder about the parental home’s environment. “Within the literature, one can find both discussions of a supportive, cohesive family as an important component, as well as conclusions that a tense, challenging home is a contributor to high levels of achievement,” according to Schader. “Although parent variables such as educational attainment, economic status, parenting style, and energy devoted to talent development appear to explain achievement in some children, the results are not consistent, even within families.” 

Schader as well as other gifted education scholars believe that the topic of “parenting gifted children” is worthy of further review and research. As a parent, I personally subscribe to an approach whereby nurture, structure, and latitude are given at consistently high levels. It is the fine interplay between structure and latitude that I find particularly interesting in working with gifted children. As parents, we are surely able to have influence on a child’s learning, and, according to Schader, there is research that suggests that “parents of gifted children discuss and explain rather than direct.”