A descriptive and evaluative bibliography of mathematics filmstrips.

Submitted by A.W. Clark and R.W. Allen for the degree of Master of Arts and by C.H. Gardner and R.F. Sweeney for the degree of Master of Education. Thesis (Ed.M.)--Boston UniversityThe purpose of this paper is to present in one volume (1) a bibliography of all mathematics filmstrips from those suitable for the first grade to those suitable for use in senior high school and college, (2) an accurate description of each filmstrip, and (3) unbiased evaluations of each filmstrip by qualified teachers invited to take part in the project. Concomitant problems. The foregoing three parts were the heart of the problem and the portion nearly completely solved. There were, however, concomitant problems which have been partially solved by this work. The first of these concerns the limited use of filmstrips by mathematics teachers. Undoubtedly many do not believe in using filmstrips in mathematics classes. Others have never given serious thought about the advisability of using filmstrips. In later sections of this chapter and throughout this work evidence is cited to support the contention that filmstrips should have serious consideration, and that they are useful in mathematics classes. The second concomitant problem concerns the revision of current filmstrips and production of new ones. The filmstrip producers were supplied, upon their request, with summaries of the evaluations. Summaries were supplied only at the producer's request; for unless they were interested enough to request the summaries, they probably would not be interested in changing or improving their filmstrips. Summary. The problem, then, had three major parts: listing , describing, and evaluating mathematics filmstrips, and two concomitant parts: arousing the mathematics teacher's interest in filmstrips, and encouraging producers to make better productions and necessary revisions in current productions. [TRUNCATED

Summarizing and Searching Hidden-Web Databases Hierarchically Using Focused Probes

Many valuable text databases on the web have non-crawlable contents that are "hidden" behind search interfaces. Metasearchers are helpful tools for searching over many such databases at once through a unified query interface. A critical task for a metasearcher to process a query efficiently and effectively is the selection of the most promising databases for the query, a task that typically relies on statistical summaries of the database contents. Unfortunately, web-accessible text databases do not generally export content summaries. In this paper, we present an algorithm to derive content summaries from "uncooperative" databases by using "focused query probes," which adaptively zoom in on and extract documents that are representative of the topic coverage of the databases. The content summaries that result from this algorithm are efficient to derive and more accurate than those from previously proposed probing techniques for content-summary extraction. We also present a novel database selection algorithm that exploits both the extracted content summaries and a hierarchical classification of the databases, automatically derived during probing, to produce accurate results even for imperfect content summaries. Finally, we evaluate our techniques thoroughly using a variety of databases, including 50 real web-accessible text databases

Local and Global Explanations of Agent Behavior: Integrating Strategy Summaries with Saliency Maps

With advances in reinforcement learning (RL), agents are now being developed in high-stakes application domains such as healthcare and transportation. Explaining the behavior of these agents is challenging, as the environments in which they act have large state spaces, and their decision-making can be affected by delayed rewards, making it difficult to analyze their behavior. To address this problem, several approaches have been developed. Some approaches attempt to convey the $\textit{global}$ behavior of the agent, describing the actions it takes in different states. Other approaches devised $\textit{local}$ explanations which provide information regarding the agent's decision-making in a particular state. In this paper, we combine global and local explanation methods, and evaluate their joint and separate contributions, providing (to the best of our knowledge) the first user study of combined local and global explanations for RL agents. Specifically, we augment strategy summaries that extract important trajectories of states from simulations of the agent with saliency maps which show what information the agent attends to. Our results show that the choice of what states to include in the summary (global information) strongly affects people's understanding of agents: participants shown summaries that included important states significantly outperformed participants who were presented with agent behavior in a randomly set of chosen world-states. We find mixed results with respect to augmenting demonstrations with saliency maps (local information), as the addition of saliency maps did not significantly improve performance in most cases. However, we do find some evidence that saliency maps can help users better understand what information the agent relies on in its decision making, suggesting avenues for future work that can further improve explanations of RL agents

Classification-Aware Hidden-Web Text Database Selection,

Many valuable text databases on the web have noncrawlable contents that are “hidden” behind search interfaces. Metasearchers are helpful tools for searching over multiple such “hidden-web” text databases at once through a unified query interface. An important step in the metasearching process is database selection, or determining which databases are the most relevant for a given user query. The state-of-the-art database selection techniques rely on statistical summaries of the database contents, generally including the database vocabulary and associated word frequencies. Unfortunately, hidden-web text databases typically do not export such summaries, so previous research has developed algorithms for constructing approximate content summaries from document samples extracted from the databases via querying.We present a novel “focused-probing” sampling algorithm that detects the topics covered in a database and adaptively extracts documents that are representative of the topic coverage of the database. Our algorithm is the first to construct content summaries that include the frequencies of the words in the database. Unfortunately, Zipf’s law practically guarantees that for any relatively large database, content summaries built from moderately sized document samples will fail to cover many low-frequency words; in turn, incomplete content summaries might negatively affect the database selection process, especially for short queries with infrequent words. To enhance the sparse document samples and improve the database selection decisions, we exploit the fact that topically similar databases tend to have similar vocabularies, so samples extracted from databases with a similar topical focus can complement each other. We have developed two database selection algorithms that exploit this observation. The first algorithm proceeds hierarchically and selects the best categories for a query, and then sends the query to the appropriate databases in the chosen categories. The second algorithm uses “shrinkage,” a statistical technique for improving parameter estimation in the face of sparse data, to enhance the database content summaries with category-specific words.We describe how to modify existing database selection algorithms to adaptively decide (at runtime) whether shrinkage is beneficial for a query. A thorough evaluation over a variety of databases, including 315 real web databases as well as TREC data, suggests that the proposed sampling methods generate high-quality content summaries and that the database selection algorithms produce significantly more relevant database selection decisions and overall search results than existing algorithms.NYU, Stern School of Business, IOMS Department, Center for Digital Economy Researc