by Jaret Hodges, Ph.D.
Academics have many terms with which to describe why identifying students as twice exceptional is difficult: non-linear decision surfaces; non-convex class separation, and (one of my favorites) non-linear discriminant structures. All these are fancy ways of saying that the traits of twice-exceptional students overlap with the traits of gifted students and those with exceptionalities. In essence, identifying a child as twice exceptional can be a bit of a Gordian knot. Understanding why it’s hard to identify these students can help parents be better advocates for their children. This small blog will give a short introduction into the quantitative reasons that identifying twice exceptional students is difficult.
One of the critical applications of modern mathematics is classification. A tremendous amount of academic brainpower went into this process. It involves being able to separate a set of objects into different groups. Sometimes this is a relatively simple task. For example, my wife and daughter use simple heuristics to determine whether they will eat a given skittle: if the skittle is red or purple, they eat it; if it’s not, it goes in the trash. Classification can also be far more complex, such as machine learning techniques like convolutional neural networks that can determine whether a given response to a Facebook post agreed or disagreed with the original post. In mathematics and machine learning, the simplest classification problems involve drawing nice, crisp boundaries: this side is Group A, and that side is Group B (e.g., red/purple here; not red/purple there).
Things become more complicated when the boundary between one group and another stops being a simple straight line. Consider a school district that uses a single test for identification. If a student scores above the test threshold, they are identified. That constitutes straight line separation.
To identify twice exceptional students, you need something called a curved boundary (and sometimes more than one curve). A twice exceptional student might be mathematically gifted but have dyscalculia that is suppressing their mathematical gifts. A test, with simple line separation, cannot disentangle the dyscalculia from the mathematical gifts or the dyslexia from the verbal abilities. Nonlinear separability rises forth.
In reality, you can’t cleanly separate the groups with a single cut score or a single rule. Rather, a school district must use a flexible boundary that twists and turns to capture how strengths and challenges interact. Most school district gifted identification procedures, however, aren’t really built with that kind of complexity in mind. They use checklists, percentiles, and thresholds. These all make the assumption that every trait pushes a student in one direction only. Obviously, twice-exceptional students violate that assumption. Their strengths can mask their disabilities, and their disabilities can mask their strengths, creating patterns that don’t match either category.
Thus do gifted education evaluation committees disagree, scores can/do look inconsistent, and a child can excel in one domain while struggling in another. From a mathematical standpoint, twice-exceptional students sit in the intersection of overlapping curves. Step one is recognizing those curves so that those students are appropriately supported.
Gifted Education Family Network 