Haolin Feng | Searcharxiv

arXiv2026

Detective scaffolding for within-session reasoning development: a three-phase framework evaluated in polymer engineering and pre-university outreach

This paper presents a detective scaffolding framework -- a three-phase instructional sequence (Hypothesis Activation -> Evidence Structuring -> Causal Integration) in which engineering students investigate a realistic industrial defect scenario using staged in-class polls as designed evidence probes. Unlike conventional uses of student response systems for engagement, the framework positions each poll as an Evidence-Centred Design instrument targeting a specific reasoning capability. In the primary implementation, 80 Year~3 polymer engineering students progressed from prior-knowledge-driven misconception (71% attributing defects to temperature) to complete root-cause convergence (100\% identifying humidity; Fisher's exact test, $p < .001$) across four sequenced prompts within a single 90-minute lecture slot. A dual-accuracy analysis revealed that at one intermediate stage, textbook-correct and analytically valid responses diverged, illustrating why conventional scoring can misrepresent reasoning quality. In a transferability study, 26 Year~12 students with no engineering background achieved identical root-cause identification rates across two adapted scenarios, with significant gains in data-analysis confidence and AI explanation ability. The results suggest that the pedagogical structure, rather than disciplinary content, drives the convergence effect, implying portability across disciplines and educational levels.

physics.ed-ph↗

arXiv2016

Optimal Control of a Levy Inventory System: The Optimality of Control Band Policy

We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred continuously at some rate as a function of the inventory state. The inventory control costs, incurred only when interventions of the inventory state are placed, have both a fixed and a variable component. The objective is to minimize the expectation of the infinite horizon discounted costs. We formulate this as a stochastic impulse control problem. In our setting, we obtain analytical results that are of significant implications. Specifically, we establish the existence of the optimal control, and we provide the solution in closed-form. More importantly, we prove the optimality of the simple control band policy. Furthermore, we investigate the transient and the steady-state behavior of the controlled process and the stochastic decomposition property.

math.OC↗