arXiv subjects

Jeffrey Matayoshi

Publications and source records attributed to Jeffrey Matayoshi.

3 recordsLinked to original sources

arXiv2026

Faster Completion, Less Learning: Generative AI Reduced Study Time on Math Problems and the Knowledge They Build

How much have students' ordinary learning processes shifted in response to generative AI, and how does that affect their durable learning outcomes? Self-report surveys show little change, while small-scale behavioral studies report widespread AI use without the scale or duration to measure learning consequences. We address both questions using a ten-year panel of $3.2$ million ALEKS learning interactions for investigating time-on-task, complemented by ALEKS PPL placement-assessment data for examining proctoring and learning outcomes, with a quasi-experimental design exploiting variation in tasks that are more susceptible to AI (text-based word problems) and less susceptible to AI (interactive graph-based problems). Learning time on AI-susceptible problems declines $2.8\%$ per quarter among college students after ChatGPT's release, cumulating to $26.9\%$ over eleven quarters; high-schoolers show $31.3\%$, middle-schoolers $9.0\%$, and Grade 5 students no detectable change. Among college students, the post-ChatGPT divergence vanishes entirely under proctoring, ruling out broad efficiency gains as the likely explanation. Logistic fixed-effects models on randomly assigned proctored retention items yield a $25\%$ cumulative decline in odds of correct response; the same estimator on non-proctored assessment produces a large opposite-signed increase -- inconsistent with any platform, cohort, or curriculum explanation. These results are among the first large-scale behavioral and outcome evidence that generative AI has altered how students study and the knowledge they build -- the population-level indicator of \emph{cognitive surrender}, with direct implications for educational research, assessment governance, and AI policy.

cs.CY↗

arXiv2010

The real zeros of a random algebraic polynomial with dependent coefficients

Mark Kac gave one of the first results analyzing random polynomial zeros. He considered the case of independent standard normal coefficients and was able to show that the expected number of real zeros for a degree n polynomial is on the order of (2/pi)log(n), as n goes to infinity. Several years later, Sambandham considered two cases with some dependence assumed among the coefficients. The first case looked at coefficients with an exponentially decaying covariance function, while the second assumed a constant covariance. He showed that the expectation of the number of real zeros for an exponentially decaying covariance matches the independent case, while having a constant covariance reduces the expected number of zeros in half. In this paper we will apply techniques similar to Sambandham's and extend his results to a wider class of covariance functions. Under certain restrictions on the spectral density, we will show that the order of the expected number of real zeros remains the same as in the independent case.

math.PR↗

arXiv2009

The K-level crossings of a random algebraic polynomial with dependent coefficients

For a random polynomial with standard normal coefficients, two cases of the K-level crossings have been considered by Farahmand. When the coefficients are independent, Farahmand was able to derive an asymptotic value for the expected number of level crossings, even if K is allowed to grow to infinity. Alternatively, it was shown that when the coefficients have a constant covariance, the expected number of level crossings is reduced by half. In this paper we are interested in studying the behavior for dependent standard normal coefficients where the covariance is decaying and no longer constant. Using techniques similar to those of Farahmand, we will be able to show that for a wide range of covariance functions behavior similar to the independent case can be expected.

math.PR↗