Aug 2026· Riemann: Research of Mathematics and Mathematics Education· 0 citations· 33 references
TL;DR
The findings indicate that anchoring experiential loops within a scannable digital format systematically drives uniform cognitive gains, offering a robust pedagogical vehicle for vocational mathematics education.
Abstract
Mathematical critical thinking skills are essential for vocational students, yet traditional instruction often struggles to teach abstract deductive proofs within rigid school schedules. While digital media is widely used, there remains a pedagogical gap in integrating structured experiential cycles into interactive platforms to foster higher-order reasoning. This study aims to develop and evaluate an interactive flipbook integrated with Kolb’s experiential learning model to address this limitation. Utilizing the 4D development method (Define, Design, Develop, Disseminate), the platform's operational practicality was evaluated by teaching practitioners and a small group of 20 students, followed by a field implementation phase with a cohort of 30 vocational students (N = 30) facing mathematical induction topics. Data were gathered through expert validation sheets, teacher practicality questionnaires, and critical thinking pre-/post-tests. The results demonstrate that the developed media achieved excellent expert validity across content, media, and language parameters. Furthermore, it attained a high operational practicality rate of 84.00% from teaching practitioners, acting as an autonomous scaffolding tool. Importantly, the media proved highly effective, yielding an overall student critical thinking score of 79.00%, with peak performance in variable identification (90.00%) and argument validation (88.00%). These findings indicate that anchoring experiential loops within a scannable digital format systematically drives uniform cognitive gains, offering a robust pedagogical vehicle for vocational mathematics education.
FLARE is proposed, a novel framework that endows VLAs with robust error recovery capabilities through a ``Retry" and ``Reset" Paradigm, and significantly improves task success and robustness.
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Experimental results show that CritICL consistently outperforms standard in-context learning and achieves performance competitive with or superior to test-time scaling methods, while requiring significantly fewer generations and lower token cost.
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Chen Xia, Tong Gou, Yinliang Xu et al.· IEEE Transactions on Smart G...· 1 citation
General-purpose language models can reason and synthesize knowledge, but complex work also requires sustained interaction with files, information sources, and executable code, together with state maintenance, failure recovery, and verifiable delivery. We call this \emph{working capability}: sustained, verifiable progress toward a real-world objective. Apodex 1.1 develops this capability along two complementary dimensions. \emph{Environment Scaling} expands the diversity and verifiability of executable file, search, and code environments, while \emph{Agentic Coordination Scaling} trains agents to decompose long-horizon tasks, delegate parallel work, integrate asynchronous results, and replan. A shared execution harness and AgentOS maintain task state and provenance across tools and agents, and training turns environment trajectories and coordination traces into reliable behavior. Across complex professional work, finance, scientific research, mathematics, coding, and search, Apodex 1.1 reaches the leading performance band despite using a substantially smaller model than many frontier systems. The 35B-parameter Apodex 1.1 Mini further retains strong working capability in a locally deployable form. These results ground agentic intelligence in useful, verifiable work completed over time and advance our goal of building a \emph{Heavy-Duty Solver} for ambitious, long-running tasks.
Apodex Team B. An, B. Li, B. Wang et al.· 1 citation
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
