Case Study: Gaps in Learning


As a freshman, Carmen came to us with above-average grades in regular-level math and science courses at an elite prep school. As a reasonably organized student, she seemed content with her track, but her parents wondered what it would take for her to progress to the honors/AP level. Our tutor’s first order of business was to assess whether Carmen was sitting on untapped potential, as her parents suggested, or if an underlying issue was holding Carmen back.

The Challenge

During their first meeting, Carmen and her tutor reviewed Carmen’s recent Algebra II and science homework and exams, and attempted some practice math problems from an SAT. The tutor noticed that Carmen had very little trouble with symbolic algebra, but reached for a calculator as soon as even the simplest of computations was required. Two issues were at play: Carmen had no confidence in her ability to do mental arithmetic, and she was actually losing time on tests in both math and chemistry by punching numbers into a calculator instead of equipping herself with some mental math skills. As a result, she lacked any sort of intuition when it came to manipulating numbers, estimating with orders of magnitude, or using operators like exponents, logarithms, and basic trigonometry functions.

The Signet Solution

Carmen’s tutor set aside several problems on which she could not use a calculator and observed as Carmen struggled to solve problems using a pencil and paper. With practice and guidance from her tutor, Carmen eventually grew faster at calculating by hand and in her head. Her tutor also framed their weekly 90-minute tutoring sessions as previews of what she’d be covering next week in her class, rather than reviews of what had already been presented. Carmen’s tutor found ways to relate her math topics to her science topics and vice versa in order to reinforce the material and keep Carmen interested. He mapped the flight of a projectile to enhance Carmen’s study of parabolas and measured the pH of serial dilutions of household cleaning supplies in order to teach logarithms.

Through working with her Signet tutor, Carmen stopped reaching for the calculator and started to value a deeper understanding of the concepts she was studying. She quickly realized that the pace at which material was delivered in her regular classes was actually painfully slow compared to what she could handle. By mid-year, her progress reports showed her at the top of her classes, and she made the leap from regular Algebra II to Honors Pre-calculus and from regular chemistry to AP Biology the following year.

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