Why and how mathematicians read proofs: an exploratory study

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, Journal for Research in Mathematics Education 39:431–459, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line-by-line reading, and modular reading. We argue that non-deductive reasoning plays an important role in each of these three strategies.     

Bowling ball dynamics revealed by miniature wireless MEMS inertial measurement unit

This paper presents a novel sensor technology to deduce the dynamics of a bowling ball. The sensor, a miniature wireless inertial measurement unit (IMU), incorporates MEMS accelerometers and angular rate gyros, a microcontroller, a low power RF transceiver, and a rechargeable battery. When embedded in a bowling ball, the IMU transmits the acceleration and angular velocity data that define the dynamics of the ball starting with the bowler’s delivery and its motion in the lane. Example results from professional bowlers illustrate how this technology can be used to assess bowler skill and ball performance. For instance, the IMU accurately measures the spin dynamics of the ball which are crucial to develop the ball “hook.” An analysis of ball dynamics in the lane is distilled to a measurable “hook potential” metric for further assessing bowler skill. Finally, the sensor presented herein is believed to be the world’s smallest, wireless IMU. This highly miniaturized and wireless design will enable parallel training systems for many sports, including basketball, baseball, crew, cricket, golf, fly fishing, soccer, softball, tennis, rowing, among others.     

Learning in the practicum: engaging pre-service teachers in reflective practice in the online space

It is argued that online discussion is a useful tool for creating opportunities for learning in teacher education. In a project designed to improve the practicum in rural areas, researchers placed pre-service teachers (PSTs) in two different moderated online discussion forums: an unstructured personal blog space and a structured threaded discussion forum where discussion topics guided them to reflect on their practicum experiences in relation to theoretical components of their studies. Findings indicated a marked difference in the contributions made to each form of online discussion with significantly greater participation in the unstructured blog format. Using Kreber and Cranton’s hierarchy of reflection, analyses of both forums found that PSTs rarely engaged in high-level reflection. Examination of lecturer involvement in the forums suggests that their contributions did not sufficiently encourage PSTs towards optimum critical reflection. These results leave the researchers considering ways in which the practicum experience can better promote reflective practice in this crucial, component of teacher education.     

The polyadenylation code: a unified model for the regulation of mRNA alternative polyadenylation

The majority of eukaryotic genes produce multiple mRNA isoforms with distinct 3′ ends through a process called mRNA alternative polyadenylation (APA). Recent studies have demonstrated that APA is dynamically regulated during development and in response to environmental stimuli. A number of mechanisms have been described for APA regulation. In this review, we attempt to integrate all the known mechanisms into a unified model. This model not only explains most of previous results, but also provides testable predictions that will improve our understanding of the mechanistic details of APA regulation. Finally, we briefly discuss the known and putative functions of APA regulation.     

Teacher behavior, student interest and affective learning: putting theory to practice

Students of Project Adapt (PA), an instructional program for at-risk middle school students in Brooklyn NY, have displayed startling improvement on cognitive outcome measures. Teacher given grades and standardized tests illuminate the progress students have made since entering the program. The current investigation attempts to analyze PA on students' affective responses in a pre/post-test experimental design. Upon entering PA, students completed measures of interest, affect, and their previous teachers' behavior (pre). These ratings were then compared to end of year ratings on the same instruments (post). Results indicate students' perceive PA teachers utilizing different behaviors than their previous teachers. Additionally, student affect and interest increased significantly. Results of this study have implications for both instructional researchers and educational practitioners.