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Experienced provers employ a host of skills when assessing the validity of a justification, often without names for those skills. This paper offers an introduction to a lens called Toulmin analysis that can help make sense of this process. Then this paper describes both an in-class module to help students learn to apply Toulmin analysis and multiple ways this module can be integrated into courses for mathematics majors and non-majors. Toulmin analysis has helped us bring human dimensions of proving to the surface in our classrooms, and it helps us build stronger and more inclusive entryways for students into mathematical communities. Learning about Toulmin analysis helps our students connect mathematical reasoning to other thinking, supporting transfer in both directions, and it has changed our thinking about the teaching and learning of mathematics even in contexts where we do not devote class time to this model overtly.

Several major themes related to rethinking assessment emerged from a search of the papers published in "PRIMUS." Authors explored ways to change the stakes of assessments, often with outcomes-based grading and testing structures. They explored changing the "structure" of assessments by considering media beyond written exams and by configuring them as group activities. They explored ways to change the "focus" of their assessments by asking students to synthesize and engage messy applications/projects and by making metacognition part or all of the assessment activities. And they explored issues around "assessment" as part of a larger system by considering approaches to grading in general, alignment with other course activities, workload, and perceptions and expectations about assessment in mathematics. In this "PRIMUS" Curated Collection, I discuss these themes and offer some editorial perspective.

This paper reports a study of university students' experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor's degree in mathematics to be followed by a year-long teacher education credential program. The analysis of students' end of course presentations and written portfolios is framed with community of practice theory, complemented with analytic categories from community of inquiry, including notions of inquiry stance and critical alignment. Our social theorization of university mathematics education adds a complementary perspective to the more conventional cognitive and discursive analyses and is necessitated by the very nature of inquiry approaches to education. The analysis of students' presentations and writing leads to exploring their development of the notion of critical stance, which the students are seen to take toward the mathematics, their learning, and approaches to teaching mathematics. We find that the notion of critical stance can be distilled into three components: awareness, self-evaluation, and agency.

Obtaining high-resolution, spherical phoneme-dependent directivities for voice radiation is beneficial for numerous acoustics applications. This work reports on a spherical interpolation method based on two interleaved measurements using a regularized least-squares fit with reference data. Maximizing the spherical correlation between previously reported results and measured data determines the regularization hyper-parameters to ensure physical solutions. While the resultant spherical directivity patterns show similarities to time-averaged results, distinct radiation characteristics appear, particularly in the range of 630 Hz to 2 kHz.

A listening test was performed to determine whether there were any perceived differences in the playing styles of musicians as a function of the room in which the music was performed. This listening test was part of a larger study aimed at investigating the impact of room acoustics on historically informed performance (HIP) of baroque music which included an objective analysis framework designed to capture dimensions of performance important to a historical baroque playing style. The test included both flute and viol examples and included the participation of 20 musically trained listeners with a background in HIP. The results of the test showed some significant differences in certain performance parameters for both instruments. In particular, the flute examples demonstrated differences that aligned with reports from the flutists about the strategies they used to adapt to the different acoustics, and there was agreement between listener ratings and previously extracted objective parameters. These findings suggest that room acoustics play a role in shaping musical performance, and that the resulting changes can be perceived by listeners.

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration into courses, reflection on ways to leverage the activity for discussion with students at the start of a course about the nature of mathematical inquiry and norms for learning through inquiry. [ABSTRACT FROM AUTHOR]

Previous studies have discussed six pre-Sabine quantifiable guidelines employed in room acoustic design: voice directivity, audience rake, “echo theory”, stage acoustics, reverberation, and length, width, and height ratios. Around the turn of the 18th century, these notions led to two shapes that were theoretically regarded optimal for rooms with acoustical demands: ellipse and semi-circle. The first of these shapes to be tested was the ellipse in the design for the Iffland Theatre (1802–1817). As the resulting acoustics were notoriously poor, contemporary architects and acousticians discussed the grounds for the failed acoustics as well as possible corrections. Multiple subsequent halls were also based on lessons learned from this acoustic failure. As part of this archaeoacoustics research, geometric acoustic numerical simulations were employed to estimate the actual and renovated room acoustic conditions. Three configurations of the hall have been reconstructed. Results show that the hall’s shape led to sound focusing and that the rounded proscenium arch likely induced echoes. Proposed solutions of the time to increase the scattering or absorption appear unlikely to have solved the observed acoustic problems.

This study examines the efficiency of a training protocol using a virtual reality application designed to accelerate individual’s selection of, and accommodation to, non-individualized HRTF profiles. This training introduces three elements to hasten audio localization performance improvement: an interactive HRTF selection method, a parametric training program based on active learning, and a relatively dry room acoustic simulation designed to increase the quantity of spatial cues presented. Participants rapidly selected an HRTF (≈5 min) followed by training over three sessions of 12 min distributed over 5 days. To study the impact of the room acoustic component on localization performance evolution, participants were divided into two groups: one acting as control reference, training with only anechoic renderings, the other training in reverberant conditions. The efficiency of the training program was assessed across groups and the entire protocol was assessed through direct comparisons with results reported in previous studies. Results indicate that the proposed training program led to improved learning rates compared to that of previous studies, and that the included room response accelerated the learning process.

We have used wiki technology to support large-scale, collaborative writing projects in which the students build reference texts (called WikiTextbooks). The goal of this paper is to prepare readers to adapt this idea for their own courses. We give examples of the implementation of WikiTextbooks in a variety of courses, including lecture and discovery-based courses. We discuss the kinds of challenges that WikiTextbooks address and focus on critical design decisions. Finally, we conclude with a suggested template wiki project that is approachable for new users and appropriate for many course structures.

The present study tested for mediators of the relation between neighborhood risk characteristics and internalizing and externalizing symptoms in a sample of 1,120 low-income urban adolescents. Results indicate that a composite of census tract variables predicted both internalizing and externalizing symptoms in this sample. Stressful life events and exposure to violence mediated the relation between neighborhood risk and aggression, delinquency, and somatic symptoms. Gender and age were examined as moderators of these mediational pathways. Results of moderated mediation analyses revealed that both gender and age moderated the pathways between stressors and somatic complaints and between exposure to violence and somatic complaints. Implications for intervention and areas for future research are discussed. (Contains 1 note, 2 figures, and 5 tables.)

The purpose of this study was to evaluate a brief version of the Alcohol Expectancy Questionnaire-Adolescent (AEQ-A; Brown, Christiansen, & Goldman, 1987). The original AEQ-A was reduced to seven items (called the AEQ-AB). Principal Components Analysis (PCA) was performed and two factors emerged (General Positive Effects and Potential Negative Effects) accounting for 46% of the variance. Internal consistencies are comparable to those of the original AEQ-A (0.50). Scales correlate with criterion variables such as average drinks per week and average number of drinks per heavy drinking day (p less than 0.05). It is concluded that this questionnaire may be useful to clinicians providing brief assessment and intervention. Cross-validation in other samples and other settings is recommended.

Rates and cooccurrence of internalizing and externalizing syndromes were examined in a sample of 1,520 low-income urban early adolescents. Results indicate higher rates of clinically elevated internalizing and externalizing symptoms in this sample relative to normative data. In particular, both boys and girls were more likely to score in the clinical range on the broad-band internalizing and externalizing subscales of the Youth Self-Report and on the anxious-depressed, withdrawn, somatic, delinquency, and aggression narrow-band subscales. Girls reported higher rates of internalizing symptoms on the broad-band internalizing subscale and on narrow-band anxious-depressed, withdrawn, and somatic complaints subscales. Contrary to expected, boys did not report higher rates of externalizing symptoms on any of the externalizing subscales. Results of bidirectional comorbidity analyses indicate that cooccurrence of aggressive with somatic symptoms and cooccurrence of aggressive with delinquency symptoms were significantly more common in this sample than in normative samples.