The promises of numeracy

The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4–7 students’ thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative analysis of the data yielded four distinct groups of students demonstrating a wide range of performance in these tasks. Qualitative analysis of students’ solutions provided further insight into their understanding of basic algebraic concepts, and the nature of the processes and forms of reasoning they utilized. The results showed that students in each group were able to solve different number and types of tasks, using different strategies. Results also indicated that students from all grades were present in each group. These findings suggest the presence of a consistent trend in the difficulty level across early algebraic tasks which may support the existence of a specific developmental trend from more intuitive types of early algebraic thinking to more sophisticated ones.     

Depressed Mothers' Touching Increases Infants' Positive Affect and Attention in Still-Face Interactions

The effects of depressed mothers' touching on their infants' behavior were investigated during the still-face situation. 48 depressed and nondepressed mothers and their 3-month-old infants were randomly assigned to control and experimental conditions. 4 successive 90-sec periods were implemented: (A) normal play, (B) still-face-no-touch, (C) still-face-with-touch, and (A) normal play. Depressed and nondepressed mothers were instructed and shown how to provide touch for their infants during the still-face-with-touch period. Different affective and attentive responses of the infants of depressed versus the infants of nondepressed mothers were observed. Infants of depressed mothers showed more positive affect (smiles and vocalizations) and gazed more at their mothers' hands during the still-face-with-touch period than the infants of nondepressed mothers, who grimaced, cried, and gazed away from their mothers' faces more often. The results suggest that by providing touch stimulation for their infants, the depressed mothers can increase infant positive affect and attention and, in this way, compensate for negative effects often resulting from their typical lack of affectivity (flat facial and vocal expressions) during interactions     

The Impact of Reform: Challenges for Mathematics Teacher Preparation

The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated, what has yet to be fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation.     

Effects of learner–instructor relationship-building strategies in online video instruction

Although research has demonstrated that an increased rapport between instructors and learners can positively relate with increased learning gains, perhaps mediated by the positive attitudes toward the course and self-efficacy beliefs in the coursework, little has been done to test what instructional strategies might increase this rapport in online video-based instruction. This study compared online video-based instruction that made use of relationship-building strategies with online video-based instruction that did not use those strategies. The two instructions were identical in every other way. The results show that the attitudes of the college students were positively affected by the relationship building strategies in a statistically significant way (p = .025) and that learning gains were also positively affected at a very near-significant level (p = .052). The implications of the findings are discussed.     

Curiosity and openmindedness in open and traditional classrooms

In an attempt to determine if an open classroom environment encourages greater curiosity and/or openmindedness than does a traditional classroom environment, 41 open classroom children and 42 traditional classroom children completed an openmindedness scale and 5 subtests of a curiosity scale. Sex was included as a factor and IQ was included as a covariate in all analyses. No significant sex differences were found. The significantly higher mean curiosity score for the open classroom group was primarily due to significant differences between classrooms on 2 of the subtests: those measuring preference for novelty and change (p <.05). The results were interpreted as an indication that the open classroom may encourage some aspects of curiosity to a greater extent than does the traditional classroom.     

The effect of a human agent’s external regulation upon college students’ hypermedia learning

In this study we examined the effectiveness of self-regulated learning (SRL) and externally regulated learning (ERL) on college students’ learning about a science topic with hypermedia during a 40-min session. A total of 82 college students with little knowledge of the topic were randomly assigned either to the SRL or ERL condition. Students in the SRL condition regulated their own learning, while students in the ERL condition had access to a human tutor who facilitated their self-regulated learning. We converged product (pretest–posttest declarative knowledge and qualitative shifts in participants’ mental models) with process (think-aloud) data to examine the effectiveness of SRL versus ERL. Analysis of the declarative knowledge measures showed that the ERL condition group mean was statistically significantly higher than the group mean for the SRL condition on the labeling and flow diagram tasks. There were no statistically significant differences between groups on the matching task, but both groups showed statistically significant increases in performance. Further analyses showed that the odds of being in a higher mental model posttest group were decreased by 65% for the SRL group as compared to the ERL group. In terms of SRL behavior, participants in the SRL condition engaged in more use of selecting new information sources, re-reading, summarizing, free searching, and enacting control over the context of their learning. In comparison, the ERL participants engaged in more activation of prior knowledge, utilization of feeling of knowing and judgment of learning, monitoring their progress toward goals, drawing, hypothesizing, coordination of information sources, and expressing task difficulty. An earlier version of this paper was presented at the international conference of Artificial Intelligence in Education (AI-Ed 2007), Los Angeles, LA (July, 2007).     

Analyzing Contemporary Introductory Textbooks on Correctional Administration/Management/Organization: A Content Analysis

This book review essay discusses and analyzes how introductory textbooks on correctional administration, written primarily for the American university market, frame the discourse on this subject matter. The writer presents both quantitative and qualitative empirical evidence of coverage given to prison administration. In addition to traditional content analysis methods, the authors of these books were contacted and asked to explain the decision‐making processes they used for content inclusion, exclusion and/or minimization. The paper concludes with a handful of recommendations on improving texts in this subdiscipline.