Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

Social working memory: Memory for another rat's spatial choices can increase or decrease choice tendencies

In two experiments using a radial-arm maze, pairs of rats made choices among eight maze locations, each containing a large quantity of one of two food types. The choices made by 1 rat affected the choices made by the other rat. Under most conditions, visits by 1 rat increased the tendency of the other rat to subsequently choose that maze location. However, the effect depended on the quality of the food available in a particular location. When it was possible for the rats to observe each other on the maze arms and a rat had experienced that a location contained the less preferred food type, a previous visit to that location by the foraging partner decreased the tendency to visit that location. These effects are attributed to working memory for the spatial choices of another rat, and they indicate that memory produced by a rat’s own visit to a maze location is integrated with memory for the behavior of another rat to determine spatial choice     

Relationships between student characteristics and self‐, peer and tutor evaluations of oral presentations

There are many influences on how assessors grade themselves and others. Oral presentations are useful for exploring such factors in peer, self‐ and tutor marked assessments, being rapidly completed and assessed, commonly used in HE and very difficult to anonymize. This opportunistic study examined the effects of gender and level of attainment on the triangulation of marks awarded to student presenters. Grades generated by peer assessment were associated more strongly with tutor‐awarded marks than those from self‐assessment. For self‐assessment there was a strong effect of gender (female students undervalued their performance compared with tutor grades). Peer assessment produced higher marks than from tutors, perhaps because of the close‐knit community developed during residential courses. For tutor marks, the greatest variability was at the lower end of the scale, whereas peer assessors were most variable when marking students who self‐evaluated or peer assessed highly. Students awarded a narrower range of marks to peers compared with tutors, but when self‐assessing used a larger range. Presentations by students who admitted to little sleep the night before received lower grades from both peers and tutors, but this was not reflected by self‐assessments, suggesting they were unaware of their poorer performances. Sessions with fewer talks (four rather than seven) reduced the ‘dip’ in marks previously observed in the middle of sessions. Findings are discussed in the context of bias in this mode of assessment.     

Evaluating fifth- and sixth-grade students’ expository writing: task development, scoring, and psychometric issues

Drawing from multiple theoretical frameworks representing cognitive and educational psychology, we present a writing task and scoring system for measurement of students’ informative writing. Participants in this study were 72 fifth- and sixth-grade students who wrote compositions describing real-world problems and how mathematics, science, and social studies information could be used to solve those problems. Of the 72 students, 69 were able to craft a cohesive response that not only demonstrated planning in writing structure but also elaboration of relevant knowledge in one or more domains. Many-facet Rasch Modeling (MFRM) techniques were used to examine the reliability and validity of scores for the writing rating scale. Additionally, comparison of fifth- and sixth-grade responses supported the validity of scores, as did the results of a correlational analysis with scores from an overall interest measure. Recommendations for improving writing scoring systems based on the findings of this investigation are provided.     

Play to win! Using games in library instruction to enhance student learning

Research has shown that educational games can have positive impacts on student learning and motivation. The success of a game played in a library instruction class depends on the type of game selected, the development of learning outcomes, and the flexibility of the librarian during class. This article explains the benefits to students and librarians of using games, discusses the development and use of a Jeopardy-style game, and provides practical tips for librarians interested in developing and incorporating games into one-time library instruction sessions.     

Health literacy and consumer health information

The rigours of the past few years have demonstrated the importance of good health literacy levels with the imperative of being able to obtain and interpret information to maintain and improve one's health never more apparent. With this in mind, this issue is focused on consumer health information, the gender and population group differences that exist in information seeking behaviour, the challenges of understanding medical explanations and terminology, and existing criteria to assess and ultimately produce better consumer health information.     

Comparing Web search engine performance in searching consumer health information: evaluation and recommendations.

Identifying and accessing reliable, relevant consumer health information rapidly on the Internet may challenge the health sciences librarian and layperson alike. In this study, seven search engines are compared using representative consumer health topics for their content relevancy, system features, and attributes. The paper discusses evaluation criteria; systematically compares relevant results; analyzes performance in terms of the strengths and weaknesses of the search engines; and illustrates effective search engine selection, search formulation, and strategies.     

Retrieving and classifying instances of source code plagiarism

Automatic detection of source code plagiarism is an important research field for both the commercial software industry and within the research community. Existing methods of plagiarism detection primarily involve exhaustive pairwise document comparison, which does not scale well for large software collections. To achieve scalability, we approach the problem from an information retrieval (IR) perspective. We retrieve a ranked list of candidate documents in response to a pseudo-query representation constructed from each source code document in the collection. The challenge in source code document retrieval is that the standard bag-of-words (BoW) representation model for such documents is likely to result in many false positives being retrieved, because of the use of identical programming language specific constructs and keywords. To address this problem, we make use of an abstract syntax tree (AST) representation of the source code documents. While the IR approach is efficient, it is essentially unsupervised in nature. To further improve its effectiveness, we apply a supervised classifier (pre-trained with features extracted from sample plagiarized source code pairs) on the top ranked retrieved documents. We report experiments on the SOCO-2014 dataset comprising 12K Java source files with almost 1M lines of code. Our experiments confirm that the AST based approach produces significantly better retrieval effectiveness than a standard BoW representation, i.e., the AST based approach is able to identify a higher number of plagiarized source code documents at top ranks in response to a query source code document. The supervised classifier, trained on features extracted from sample plagiarized source code pairs, is shown to effectively filter and thus further improve the ranked list of retrieved candidate plagiarized documents.     

A Theory of Media Power and a Theory of Media Use: Different Stories,Questions, and Ways of Thinking

In this article, I compare the assumptions, concepts, and propositions of media system dependency (MSD) theory and uses and gratifications (U&G) theory at the microlevel of analysis. The epistemological origins of these theories are situated within the differing social and personal contexts that affected their development. Those MSD assumptions that serve as background to this comparison are specified, and major hypotheses concerning the social ecology of microeffects processes are discussed, particularly as they pertain to public opinion concerns. Following this elaboration of MSD theory, basic differences between MSD and U&G conceptions of the audience, interpersonal networks, the media system, and the nature of media power are addressed. I conclude with a brief comment on the implications of the Internet for theorizing micro media effects.