Modernizing Proof Teaching through Viviani's Theorem

2020 ◽  
Vol 113 (10) ◽  
pp. 835-840
Author(s):  
Addie Armstrong ◽  
Dan McQuillan

Valid proofs need not be in the traditional two‐column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

1988 ◽  
Vol 27 (04) ◽  
pp. 184-186 ◽  
Author(s):  
Thomas Gjørup

SummaryThe kappa coefficient is a widely used measure of agreement between observers’ independent recording of diagnoses. Kappa adjusts the overall agreement for expected chance agreement. The dependence of kappa on the prevalence . of a diagnosis has not previously been emphasized. This dependence means that kappa does not give a general statement of the reproducibility of a diagnosis. The result of a study of observer agreement should, therefore, not – as it has been done in several studies – be given by the kappa value alone. The kappa value should always be given together with the original results of the study.


Author(s):  
Alexander H. Greer ◽  
William Vauclain ◽  
Elijah Lee ◽  
Aidan Lowe ◽  
Jared Hoefner ◽  
...  

Traditio ◽  
2018 ◽  
Vol 73 ◽  
pp. 83-116
Author(s):  
PETER O'HAGAN

Peter Lombard's influential commentary on the Pauline Epistles, theCollectanea in omnes divi Pauli epistolas,has received little extended analysis in scholarly literature, despite its recognized importance both in its own right and as key for the development of hisSentences.This article presents a new approach to studying theCollectaneaby analyzing how Lombard's commentary builds on theGlossa “Ordinaria”on the Pauline Epistles. The article argues for treating theCollectaneaas a “historical act,” focusing on how Lombard engages with the biblical text and with authoritative sources within which he encounters the same biblical text embedded. The article further argues for the necessity of turning to the manuscripts of both theCollectaneaand theGlossa,rather than continuing to rely on inadequate early modern printed editions or thePatrologia Latina.The article then uses Lombard's discussion of faith at Romans 1:17 as a case study, demonstrating the way in which Lombard begins from theGlossa,clarifies its ambiguities, and moves his analysis forward through his use of otherauctoritatesand theologicalquaestiones.A comparison with Lombard's treatment of faith in theSentenceshighlights the close links between Lombard's biblical lectures and this later work. The article concludes by arguing that scholastic biblical exegesis and theology should be treated as primarily a classroom activity, with the glossed Bible as the central focus. Discussion of Lombard's work should draw on much recent scholarship that has begun to uncover the layers of orality within the textual history of scholastic works.


1951 ◽  
Vol 5 (1) ◽  
pp. 242-243

There is given below a brief general statement of the type of treaty envisioned by the United States Government as proper to end the state of war with Japan. It is stressed that this statement is only suggestive and tentative, and does not commit the United States Government to the detailed content or wording of any future draft. It is expected that after there has been an opportunity to study this outline, there will be a series of informal discussions designed to elaborate on it and make clear any points which may be obscure at first glance.


2017 ◽  
Vol 2 (4) ◽  
pp. 281-288 ◽  
Author(s):  
Marc Hurwitz

Followership is valuable for personal and organizational success, whether success is measured by satisfaction with work, improved team relationships, obtaining promotions, or quality and quantity of work output. Furthermore, senior executives and coaches recognize it as a critical skill. Despite this, creating effective followership training in the classroom is challenging because of media messages that preference leadership, internal schemas held by students that ignore followership, and cultural biases against it. This article presents a memorable kinaesthetic, visual classroom activity that introduces followership in a theory-agnostic way. The exercise begins with students introducing each other as leaders or followers, and then debriefing that activity using the Describe, Analyze, and Evaluate methodology from multicultural training. Over a 10-year period, the exercise has successfully engaged undergraduate and graduate students, MBA candidates, and working professionals from frontline to senior management.


2009 ◽  
Vol 111 (7) ◽  
pp. 1665-1692 ◽  
Author(s):  
Sean Kelly ◽  
Julianne Turner

Background/Context A common perspective found in the literature on classroom activity structures hypothesizes that a whole-class mode of instruction is linked with increased problems of achievement motivation for low-achieving students. If whole-class methods of instruction (e.g., recitation-style question-and-answer sessions) are rich in evaluation and foster social comparisons among students, low-achieving students may become disengaged in an effort to avoid negative evaluations. It is important to consider the evidence on activity structures and engagement carefully because this perspective represents a sweeping critique, concluding essentially that the predominant mode of instruction in American schools is detrimental to achieving widespread educational success. Purpose/Objective/Research Question/Focus of Study Are whole-class modes of instruction linked with increased problems of achievement motivation and disengagement for low-achieving students? Research Design This study is a review of research on the association between student engagement and activity structure. We review both quantitative and qualitative studies investigating the link between activity structure and student engagement, with an emphasis on studies that identify an interaction between students’ level of achievement, activity structure, and engagement. In interpreting the evidence, we focus on studies of classroom discourse—particularly studies of dialogic and scaffolding instruction, which illustrate variability in the effects of whole-class instruction on student engagement. Conclusions/Recommendations Although many relationships between motivational climates and levels of engagement have been clearly documented, we find no conclusive evidence of a link between whole-class instruction and disengagement among low-achieving students. Research on classroom discourse illustrates that the activities that constitute whole-class instruction are not inherently problematic for low-achieving students and can, in fact, promote engagement.


2017 ◽  
Vol 44 (3) ◽  
pp. 250-254 ◽  
Author(s):  
Ted V. Cascio

This study assesses the effectiveness of critical thinking drills (CTDs), a repetitious classroom activity designed to improve methodological and statistical thinking in relation to psychological claims embedded in popular press articles. In each of four separate CTDs, students critically analyzed a brief article reporting a recent psychological study by answering a set of 10 critical thinking questions in relation to it. Student responses were subsequently self-scored through an instructor-led discussion session. Results showed that the average CTD score increased linearly between the first and final assessment. These results suggest that critical thinking in relation to scientific claims found in secondary source material can be successfully taught and quantitatively assessed.


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