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     

Contextual effects on predicting risk for reading difficulties in first and second grade

This study utilized early reading assessment data from a randomized trial of 210 urban and rural schools in Texas to examine contextual effects on risk prediction in first and second grade. The primary objective was to examine the roles of (a) individual differences, (b) the grade 1 classroom, and (c) the pairing of first and second grade teachers in determining grade 2 outcomes in word reading and fluency. A second objective was to investigate whether the administration format of the assessment (paper, paper plus desktop, handheld plus desktop) or the level of teacher support (web mentoring, no mentoring) moderated the prediction. These moderator variables proved not to be significant. Subsequent analyses found that a combination of student pretest and mean of pretest classroom was a better predictor than student pretest alone. Additionally, the effect of student scores varied by teacher-pair. On average, intraclass correlations (ICCs) ranged from 6% to 17%. Differences in ICCs at the classroom level were much greater than at the school level, and differences in urban schools were twice that of rural schools.     

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.     

Network member support marshaling in response to another’s relational transgression experience

Relational transgressions are emotionally difficult for those who directly experience the transgression. Less is known about how transgressions affect those located within the personal network of a relational transgression victim. This study explored how network members engaged in support marshaling in response to another’s transgression experience. Results indicate that some participants marshaled support, citing four reasons for their actions: perceived insufficiency, camaraderie, personal ramifications, and personal values. We explore these reasons for marshaling support and discuss them within the broader context of support marshaling and relational transgressions.     

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.