The language of mathematics teaching: a text mining approach to explore the zeitgeist of US mathematics education

Educational Studies in Mathematics - Exploring language provides us with one approach to better understanding the practices and beliefs of a community. With advances in...     

Metacomprehension effects situated within an anchoring and adjustment framework

Low accuracy levels are often obtained when readers are asked to predict test performance over reading materials. Three investigations further explore the information readers use to make predictions during metacomprehension. Our results show that readers’ estimates are influenced by factors such as their initial impression of the reading task, based in part on their perceptions surrounding text genre and test item type. To explain these and other published results, a new framework for investigating metacomprehension using Tversky and Kahneman’s (Science, 185:1124–1131, 1974) anchoring and adjustment heuristic as a guide is proposed. We argue that readers anchor comprehension test performance on factors such as self-perceptions of reading ability and/or perceptions of the reading task and then insufficiently adjust their predictions to reflect the demands of the specific reading task at hand such as text difficulty.     

Personal Best (PB) goal-setting enhances arithmetical problem-solving

Personal Best (PB) goals are defined as specific, challenging, and competitively self-referenced goals involving a level of performance or effort that meets or exceeds an individual’s previous best. Much of the available research underpinning arguments for PB goal-setting is self-report-based; thus, the causal effect of PB goals on learning outcomes remains in question. The present experiment examined the impact of PB goal-setting (against a no-goal condition) on 68 Year 5 and 6 schoolchildren’s problem-solving during an arithmetic fluency-building activity, SuperSpeed Math. Equivalence of the two conditions was established across a range of prior ability and self-report motivational variables, including prior mathematical ability; Personal Best, Mastery, and Performance goal orientations at the individual and classroom level; mathematics self-concept; and valuing of and interest in mathematics. Controlling for initial problem-solving performance, students who set PB goals in subsequent rounds showed a small but reliable advantage over students in the control condition. These results suggest PB goals may provide a way for students to experience both challenge and success in a range of classroom activities. Suggestions for future research based on these initial findings are made.     

On Mathematical Visualization and the Place Where We Live

This paper is a case study of how a high school student, whom we call Karen, used a computer-based tool, the Contour Analyzer, to create graphs of height vs. distance and slope vs. distance for a flat board that she positioned with different slants and orientations. With the Contour Analyzer one can generate, on a computer screen, graphs representing functions of height and slope vs. distance corresponding to a line traced along the surface of a real object. Karen was interviewed for three one-hour sessions in an individual teaching experiment. In this paper, our focus is on how Karen came to recognize by visual inspection the mathematical behavior of the slope vs. distance function corresponding to contours traced on a flat board. Karen strove to organize her visual experience by distinguishing which aspects of the board are to be noticed and which ones are to be ignored, as well as by determining the point of view that one should adopt in order to see the variation of slope along an object. We have found it inspiring to use Winnicott's (1971) ideas about transitional objects to examine the role of the graphing instrument for Karen. This theoretical background helped us to articulate a perspective on mathematical visualization that goes beyond the dualism between internal and external representations frequently assumed in the literature, and focuses on the lived-in space that Karen experienced which encompassed at once physical attributes of the tool and human possibilities of action.This revised version was published online in September 2005 with corrections to the Cover Date.     

Designing Personalized Online Teaching Professional Development through Self-Assessment

Many institutions use a one-size-fits-all approach to faculty development for online teaching, which does not meet the needs of faculty who often have different levels of experience, skill, and self-efficacy in online teaching and learning. To address these issues, the [university name removed] [center name removed] designed and implemented an online teaching readiness self-assessment. The instrument was developed based on key attributes and skills needed for proficiency in online teaching, in three areas: online teaching experience and attitudes, learning management system proficiency, and access to technology. The self-assessment was distributed through a web-based survey tool to faculty who were identified to develop new online courses. Individual results were used to create personalized frameworks of professional development offerings (workshops, institutes, videos, and consultations) and just-in-time resources to support faculty in their development process.     

Evaluating the validity of the Automated Working Memory Assessment

The aim of the present study was to investigate the construct stability and diagnostic validity of a standardised computerised tool for assessing working memory: the Automated Working Memory Assessment (AWMA). The purpose of the AWMA is to provide educators with a quick and effective tool to screen for and support those with memory impairments. Findings indicate that working memory skills in children with memory impairments are relatively stable over the course of the school year. There was also a high degree of convergence in performance between the AWMA and the WISC‐IV Working Memory Index. The educational implications are discussed.     

Democracy-Appealing Partisanship: A Situated Ideal of Citizenship

This study develops a context-grounded ideal about how citizens ought to communicate in legislative hearings about contentious issues. We begin with an overview of the dominant model of good citizen discourse, democratic deliberation, and argue why it is an inappropriate norm for public hearings in state legislative bodies. After overviewing grounded practical theory (GPT), the meta-theoretical approach used, and providing background on the demands of public meetings, we describe the public hearing that is the focal data. That hearing was the 18-hour, 2009 Hawaii hearing on a bill that proposed to recognize committed relationships of same-sex couples through civil unions. The analysis of citizen testimony evidences a discourse strategy, democracy-appealing partisanship, which speakers on both sides of the issue used to manage the challenges they confronted in speaking out. This strategy involved advocating strongly for one viewpoint as an appeal to either majority rule or minority rights and/or either freedom of religion or separation of church and state were made. In concluding, we describe the problem to which this strategy is responsive, justify the norm of democracy-appealing partisanship, and offer implications for future studies using GPT.     

An investigation of cognitive skills and behavior in high ability students

The purpose of this study was to investigate the cognitive and behavioral profiles of high ability students. Performance on measures of verbal and visuo-spatial working memory and general ability (vocabulary and block design) was compared across the following groups: high, average, and low ability students. The behavioral profile of high ability students was also compared with those with a clinical diagnosis of ADHD. The working memory performance was superior in the high ability students compared to the low and average ability groups, though the relationship between working memory and IQ weakens as a function of increasing ability. The findings are discussed in light of Spearman's law of diminishing returns. The behavioral profile of this group indicates similar features in some respects to those with a clinical diagnosis of ADHD, however, underlying explanations may differ and should be taken into consideration in future research on dual needs in high ability students.     

White children's prosocial behavior toward White versus Black peers: The role of children's effortful control and parents' implicit racial attitudes

White children's effortful control (EC), parents' implicit racial attitudes, and their interaction were examined as predictors of children's prosocial behavior toward White versus Black recipients. Data were collected from 171 White children (55% male, M_age = 7.13 years, SD = 0.92) and their parent in 2017. Prosocial behavior toward White peers was predicted by children's higher EC. When predicting prosocial behavior toward Black peers and prosocial disparity (the difference between White and Black recipients), parents' implicit racial attitudes moderated the relation between children's EC and children's prosocial behavior. Specifically, children's EC was positively associated with prosocial behavior toward Black peers (and negatively related to inequity in prosocial behavior) only when parents exhibited less implicit racial bias.