The 15-Minute Audition: Translating a Proof of Concept Into a Domain-Specific Screening Device for Mathematical Talent

Prescreening as a Device for Identifying Essential Abilities in a Domain

Choreographer Eliot Feld pursued funding to test his hypothesis that a wider range of gifted young people might be drawn to serious dance training beyond those attending programs like the School of American Ballet, the preparatory academy for the New York City Ballet (Subotnik, 2002). His expertise and experience led him to propose that three elements are absolutely necessary for professional dancers: (a) body proportions that meet the aesthetic of dance (e.g., long legs), (b) physical flexibility, and (c) outstanding physical memory. He developed a brief audition seeking these qualities from 8-year-olds in New York City schools, arguing that beyond these three elements, opportunity and drive played the major roles in achieving a successful dance career. His efforts led to the recruitment of students to a newly developed dance performance-based charter school (http://ballettechschool.org/) and its related dance company, also called Ballet Tech (http://ballettech.org/).

Domain Specificity and Domain Trajectories

In young children, giftedness can present in overall higher academic performance across the board or in the form of faster learning rates. But over time, abilities tend to differentiate and patterns of relative strengths and weaknesses predominate among more specific cognitive abilities. Research from the Study of Mathematically Precocious Youth (SMPY; Lubinski, Benbow, Webb, & Bleske-Rechek, 2006; Park, Lubinski, & Benbow, 2007; Wai, Lubinski, & Benbow, 2005) shows that outstanding physical scientists typically have a profile of higher mathematical and spatial reasoning ability compared with verbal reasoning ability, whereas equally talented individuals who enter the social sciences and humanities tend to have the opposite profile. Replications have validated the predictive validity of these domain-specific abilities for high achievement and creative productivity in adulthood (Makel, Kell, Lubinski, Putallaz, & Benbow, 2016; Park et al., 2007).

Specific abilities are relevant to potential in every domain; for example, pitch perception (Freeman, 2000) and audiation in music performance (Ruthsatz, Detterman, Griscom, & Cirullo, 2008), and intonation, timbre, and musicality in vocal performance (C. Watts, Barnes-Burroughs, Andrianopoulos, & Carr, 2003). According to Krutetskii (1976),

mental abilities that are general by nature (such as ability to generalize) in a number of cases can appear as specific abilities (the ability to generalize mathematical objects, relations, and operations). There appears to be every basis for speaking of special specific abilities and not of general abilities that are only refracted in a unique way in mathematical activity. No one will deny that there is a specific musical memory on the grounds that it is ultimately a manifestation of memory as a general property. (p. 360)

Furthermore, domains of talent have different trajectories—different starting points, peaks, and end points—and these vary within domains as well (see Figure 1; Subotnik, Olszewski-Kubilius, & Worrell, 2011). For example, in some music areas (e.g., stringed instruments) and in mathematics—talent can be evident relatively early and, consequently, instruction and more intensive talent development activities can start in elementary school.

OPEN IN VIEWER

Figure 1.

Early and later trajectories in music, athletics, and academics, within and across domains.

Children also vary in the timing of their progress through stages of talent development as a result of opportunity or changes in motivation. As we show, the literature supports indicators of talent in mathematics as early as kindergarten, and some children are ready for an advanced curriculum and accelerated placement in mathematics at the start of school or in after-school programs—because their potential has already been significantly nurtured at home or via enriched educational opportunities. Other children, as a result of poverty or other circumstances that limit their opportunities, may have exceptional learning potential that is not obvious. One of the most important challenges for our field is identifying children with potential to benefit from supplemental opportunities, particularly those children who do not have the advantage of enriched environments and exposure to talent domains at home, school, or community programs.

Notably, we do not suggest this method as a way of identifying prodigies in mathematics—these individuals will often stand out without being formally identified. Rather, we are suggesting that, modeled after Feld’s approach, this method may be useful in identifying individuals with potential in mathematics who might be otherwise overlooked. In sum, new conceptions of giftedness have focused on domain-specific talent development, whereby giftedness in a domain is first expressed as potential that gets translated into achievement, all the while keeping in mind that trajectories of different domains begin, peak, and end at different ages.

Focusing on the Domain of Mathematics

In conducting a review of background literature for the domain, we considered the following three questions. Is the domain’s trajectory one that begins during the school years? Is there a literature regarding short-term predictors of achievement in the domain that can assist with conceptualizing items for a prescreen? Is there literature on long-term predictors of achievement/creativity in careers, and any discussion of predictors that differentiate between creative products and achievement outcomes (Leikin & Lev, 2013; Leikin, Waisman, & Leikin, 2016)?

Mathematics is one of the domains where potential may be developed during the primary grades (Clements & Sarama, 2011; Louis, Feiring, & Lewis, 1992; Robinson, Abbott, Berninger, & Busse, 1996; see Figure 1), and therefore, those with propensities for mathematics can benefit from opportunities to build on their talent even in elementary school. Existing psychological science on talent in mathematics can be organized in three categories, focusing either on prediction for later school achievement or creativity in the domain:

Translating the Literature Into a Prescreening Instrument in Mathematics

The first category of the literature we presented concentrated on predicting secondary school mathematics achievement (not necessarily creativity) based on elementary school mathematics achievement. The second addressed predicting creative adult accomplishment from the middle school years. The third and final category focused on promising elementary school variables that predict or enhance the likelihood of creative mathematical outcomes in the present and into the future. In order to develop an audition/interview protocol similar to Feld’s (see Subotnik, 2002), to be used in the future by elementary school teachers who are not necessarily mathematics experts, we generated from the literature the most rudimentary abilities in the domain of mathematics. The proof of concept was framed around identifying promising candidates to participate in recreational mathematics at publicly funded after-school programs in a major metropolitan area. The constraints on the proof of concept for this project include identifying talent in recreational, creative mathematics on the part of elementary school age children using an instrument that can be easily given by a nonexpert in mathematics education. These constraints led us to generate an audition/interview based on rudimentary abilities in the domain of mathematics derived mostly from Category 3 of the literature: elementary age demonstration of mathematical creativity and a mathematical worldview.

Sorting through the literature leads us to suggest that the following variables would be the best source of items having the most promise to match student interest and untapped potential with interesting and challenging mathematical material.

For example, in exploring a mathematical cast of mind, children can be asked to recall their thoughts in response to a prompt such as a visit to a theater. According to Krutetskii (1976), such an experience might have a young person wondering about the area of the theater and how many people could be seated overall and in various sections. In contrast, children who possess different (nonmathematical) “casts of mind” might generate aesthetic responses, such as whether the theatre is attractive enough and how to make it more so. Another child might wonder what types of plays or concerts are conducted and who goes to them.

Insight and creativity (i.e., flexibility) problems that require different levels of mathematical reasoning and content knowledge are available from the work of authors like Davidson (1986), Kline (2013), Leikin (Leikin et al., 2016; Leikin & Lev, 2013), and Sriraman (2005). For the purposes of this instrument, one could employ any number of items that require keeping track of facts and being able to discard those that serve as distractors. Two problems well known in the gifted community were included in a chapter on insight and giftedness by Janet Davidson (1986, p. 207):

A third item in the project protocol would test the child’s number sense and ability to flexibly manipulate numbers to achieve a simple equation. For example, using the numbers 1 to 9 only one time each, how many ways can they create a mathematical sentence that equals zero.

Showing the ability to transform a concept into a set of symbols, such as how to convey mathematical relationships into forms understandable to others is important and challenging. One possible source of ideas for this set of items comes from the history of how mathematical systems for accounting were derived before the codification of current structures (see Ifrah, 2000). For example, ask students to pretend they are shepherds responsible for maintaining control over a herd of sheep. How could they use a simple string to keep track of their sheep and ensure none are lost?

After administering the pilot instrument during one semester of the academic year, children who demonstrate a mathematical cast of mind, and perform well on at least two of the three other items will be invited to participate in an after-school recreational mathematics club during the following semester. This second semester will be devoted to monitoring success of the identified students in the enrichment program, and using evaluation as a basis to modify the prescreen accordingly. Success would be determined in the form of student attendance, persistence, and performance, as well as teachers’ assessments of the students’ interest and learning or achievement. In the long term, with a final iteration of the instrument, the most important predictive outcome would be children’s continued enrollment and participation in enriched mathematics activities and, secondarily, school achievement and acceleration in the domain. Placing the project in a low-stakes after-school context is more likely to ensure that those who are not identified are not left believing they have no future path to enter the domain.

Summary and Conclusion

Education researchers tend to focus on interventions that will work for all children and are less inclined to consider what can be learned from the extremes of the normal distribution. Yet the outliers in a data set are often those that can provide insights into the most important questions at hand (Schaechter & Lederberg, 2004). According to Hadamard (1945),

in conformity with a rule which seems applicable to every science of observation (including mathematics), it is the exceptional phenomenon which is likely to explain the usual one. And consequently whatever we can observe that has to do with invention . . . is capable of throwing light on psychology in general.” (p. 136)

Insights into the basic abilities associated with creative mathematics can open doors to research that could break the exclusive hold of tested achievement-based identification and broaden participation in higher level mathematics.

The proof of concept presented here is based on incorporating a talent development approach to giftedness, primarily, in this case, in outside of school programming. Identifying the “drop-dead” abilities that define a potential gift and developing a mechanism for broad screening involve first analyzing which domains would be most conducive to this process. To work with children as the primary audience, that decision should be based on whether the domain has a relatively early starting trajectory. Some other early trajectory domains to explore might include poetry or engineering. Additional important factors to consider in investing in domain-specific programming include the following: Would there be more possibilities for false positives or negatives here than are tolerable for the sake of policy, and more important, for children’s self-concept?

The goal of our project is to expand the vision of domain-specific giftedness. We have proposed a procedure, like Eliot Feld’s in dance, making recruitment into the domain more practical, and one that may be broadly applied to a number of domains at appropriate starting points. In this way, a greater number of children may benefit from enriched education designed to shepherd them into the first stages of talent development.

We encourage teachers or parents to ask children what they wonder about on seeing a new structure being developed in their neighborhood. Would they be interested in how many people could enter and leave without crowding? Could it be bigger without causing imbalance in design or safety? Can they predict who would use it? The responses to these questions, if asked without priming by context (e.g., in the midst of a mathematics lesson) can offer teachers a multitude of opportunities to enrich potential abilities in mathematics, as well as to recommend children for out of school programming. Without better ways of identifying domain-specific talent, we will continue to rely on measures of general ability beyond their designed usefulness.