Counting Triples, Triangles, and Acute Triangles

1999 ◽  
Vol 92 (7) ◽  
pp. 612-619
Author(s):  
Ruth McClintock
Keyword(s):  
Problem Solving ◽  
Difference Equation ◽  
Mathematical Induction ◽  
Modular Arithmetic ◽  
Advanced Students ◽  
Greatest Integer Function ◽  
First Time

Activities involving counting triples, triangles, and acute triangles enrich the curriculum with excursions into modular arithmetic, the greatest-integer function, and summation notation. In addition, more advanced students can apply difference-equation techniques to find closed forms and can use mathematical induction to prove the formulas. Students may be learning about these topics for the first time, or they may be reviewing familiar ideas in different problem-solving contexts. In either situation, personal arsenals of problem-attacking skills are strengthened.

Sourcebook in the Mathematics of Medieval Europe and North Africa

2016 ◽  
Keyword(s):  
North Africa ◽  
Cultural Influences ◽  
Mathematical Induction ◽  
Cross Cultural ◽  
General Introduction ◽  
Extensive Survey ◽  
Medieval Europe ◽  
Ceva’S Theorem ◽  
Arabic Speaking ◽  
First Time

Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This book presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʾtaman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. The book includes a general introduction, section introductions, footnotes, and references.

Neural Correlates of Mathematical Problem Solving

2015 ◽  
Vol 25 (02) ◽  
pp. 1550004 ◽  
Author(s):  
Chun-Ling Lin ◽  
Melody Jung ◽  
Ying Choon Wu ◽  
Hsiao-Ching She ◽  
Tzyy-Ping Jung
Keyword(s):  
Problem Solving ◽  
Spectral Power ◽  
Mathematical Problem ◽  
Neural Correlates ◽  
Mathematical Problem Solving ◽  
Single Digit ◽  
Beta Power ◽  
First Time ◽  
Anterior Posterior ◽  
Arithmetical Problem Solving

This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands — θ (4–7 Hz), α (8–13 Hz) and β (14–30 Hz) — over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs — that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left–right and anterior–posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

scholarly journals Discovering and Implementing Self-Sustaining Networks of Cooperation with General Collective Intelligence

2020 ◽  
Author(s):  
Andy E Williams
Keyword(s):  
Problem Solving ◽  
General Problem ◽  
Iterative Process ◽  
Collective Intelligence ◽  
Exponential Increase ◽  
Growing Networks ◽  
First Time

Leveraging General Collective Intelligence or GCI, a platform with the potential to achieve an exponential increase in general problem-solving ability, a methodology is defined for finding potential opportunities for cooperation, as well as for negotiating and launching cooperation. This paper explores the mechanisms by which GCI enables networks of cooperation to be formed in order to increase outcomes of cooperation and in order to make that cooperation self-sustaining. And this paper explores why implementing a GCI for the first time requires designing an iterative process that self-assembles continually growing networks of cooperation.

Pindar: Selected Odes

1996 ◽  
Author(s):  
Stephen Instone
Keyword(s):  
Ancient Greece ◽  
Human Condition ◽  
Greek Text ◽  
English Poetry ◽  
Poetic Form ◽  
Advanced Students ◽  
First Time ◽  
Selection Of ◽  
The Human Condition ◽  
Sixth Form

Pindar's Odes, blending beauty of poetic form and profundity of thought, are one of the wonders of Ancient Greece. Composed in the first instance to commemorate athletics victories, they fan out like a peacock's tail to illuminate with brilliant subtlety and imagination the human condition in general, and how our moments of heroic achievement are inevitably tempered by our mortal frailties. This edition aims to make for the first time a selection of these wonderful, but complex, poems accessible and enjoyable not only to scholars and advanced students but especially to sixth-form students and non-Classicists (including anyone interested in Pindar's influence on English poetry). While particular attention is paid to elucidating Pindar's cryptic chains of thoughts and to explaining the significance of the myths in the odes, much greater help than usual in this series is given with translating the Greek. The selection, which contains Pindar's most famous poem (Olympian 1) and two particularly charming mythical stories (in Pythian 9 and Nemean 3), illustrates Pindar's range and variety by including odes commemorating victors at each of the four major games. The book presents Greek text with translation, commentary and notes.

A Note on Mathematical Induction

1974 ◽  
Vol 67 (7) ◽  
pp. 616-618
Author(s):  
Charles Brumfiel
Keyword(s):  
Mathematical Induction ◽  
Advanced Students

Do your advanced students really understand the concept of mathematical induction? Try this phony “proof” on them.

Learning Problem-Solving Skills in Algebra

1987 ◽  
Vol 15 (3) ◽  
pp. 303-324 ◽  
Author(s):  
David McArthur ◽  
Cathleen Stasz ◽  
John Y. Hotta
Keyword(s):  
Problem Solving ◽  
Learning Opportunities ◽  
Learning Problem ◽  
High Quality ◽  
Problem Solving Skills ◽  
Intelligent Tutors ◽  
Computer Tutoring ◽  
First Time ◽  
Intelligent Tutor

In this article we describe aspects of our intelligent tutor for basic algebra. A main goal of the project is to develop a computer tutoring system whose skills and knowledge approximate those of a high-quality human tutor. We are particularly interested in exploring novel learning opportunities that can be made available to students for the first time by exploiting the reactive capabilities of such intelligent tutors. In this context, we focus here on the role of an algebra expert system embedded in the tutor. We discuss how it can be used to help students learn several nontraditional types of skill and knowledge in the context of algebra, including goal-directed reasoning skills, and debugging techniques.

scholarly journals "How can you love a work, if you don't know it?": Critical Code and Design toward Participatory Digital Editions

2016 ◽  
Author(s):  
Amanda Visconti
Keyword(s):  
Problem Solving ◽  
Design Process ◽  
User Experience ◽  
Digital Humanities ◽  
Book Clubs ◽  
Textual Scholarship ◽  
Digital Edition ◽  
Introductory Section ◽  
Design Theories ◽  
First Time

This whitepaper offers an analytic discussion of the process and productfor Amanda Visconti's dissertation "How can you love a work, if you don'tknow it?": Critical Code and Design toward Participatory Digital Editions (dr.AmandaVisconti.com). The introductory section proposes a speculativeexperiment to test digital edition design theories: "What if we build adigital edition and invite everyone? What if millions of scholars,first-time readers, book clubs, teachers and their students show up andannotate a text with their infinite interpretations, questions, andcontextualizations?". Approaching digital editions as Morris Eaves'"problem-solving mechanism"s, the project designed, built, and user-testeda digital edition of James Joyce’s Ulysses with various experimentalinterface features: InfiniteUlysses.com. Three areas of research advancedthrough the project are presented: designing public and participatoryedition projects, and whether critical participation is necessary to suchprojects; designing digital edition functionalities and appearance to servea participatory audience, and what we learn about such an endeavor throughInfinite Ulysses' user experience data; and separating the values oftextual scholarship from their embodiments to imagine new types of edition.A review of theoretical and built precedents from textual scholarship,scholarly design and code projects, public and participatory humanitiesendeavors, and theories around a digital Ulysses grounds the report,followed by an overview of the features of the Infinite Ulyssesparticipatory digital edition. Section 2 discusses existing examples ofpublic participation in digital humanities (DH) projects, Section 3 focuseson digital editions and the design process, Section 4 reimagines thedigital edition by separating textual scholarship values from the commonembodiments of these values, and the conclusion sums up the interventionsof this project and lists next steps for continuing this research. Abibliography and appendices (full texts of user surveys, explanation ofproject's dissertational format, wireframes and screenshot from throughoutthe design process) conclude the report.

scholarly journals PENERAPAN MODEL PEMBELAJARAN TERPADU TIPE NESTED DALAM PEMBELAJARAN PEMECAHAN MASALAH MATEMATIKA PADA MATERI INDUKSI MATEMATIKA

2020 ◽  
Vol 6 (2) ◽  
pp. 113
Author(s):  
Aan Armini
Keyword(s):  
Problem Solving ◽  
Positive Attitude ◽  
Mathematical Problem ◽  
Learning Model ◽  
Mathematical Induction ◽  
Mathematical Problem Solving ◽  
Integrated Learning ◽  
School Year ◽  
Post Test ◽  
Students Attitudes

Through classroom action research, researchers seek to improve students 'mathematical problem solving abilities on mathematical induction material by using nested integrated learning methods and explore students' attitudes towards the application of the given learning model. The study was conducted during two cycles which included four stages of learning, namely: planning, implementation, observation, and reflection. The study was conducted in the odd semester of the 2019/2020 school year involving 34 students of class XI MIPA-2 SMAN 1 Garawangi, Kuningan. There are 2 types of research instruments used, namely tests and questionnaires. Based on the test results, it can be seen that in the post-test, the N-Gain index obtained was 0.61 (moderate). Meanwhile, based on the results of the questionnaire, it can be seen that 100% of students show a positive attitude. Thus, it can be concluded that the nested type integrated learning model can improve students' mathematical problem solving abilities on mathematical induction material and get a good appreciation with the presence of a positive attitude shown by all participants.

scholarly journals Kraepelin’s Final Views on Dementia Praecox

2020 ◽  
Author(s):  
Kenneth S Kendler
Keyword(s):  
Clinical Work ◽  
Dementia Praecox ◽  
Psychological Consequences ◽  
Case Histories ◽  
Advanced Students ◽  
Clinical Presentations ◽  
Clinical Description ◽  
First Time ◽  
Chronic Course ◽  
Original Concept

Abstract In 1921, at the age of 65, 6 years after completing the final edition of his textbook, 22 years after first proposing the concept of dementia praecox (DP), and 1 year before retiring from clinical work, Emil Kraepelin completed the last edition of his “Introduction to Clinical Psychiatry,” which contained a mini-textbook for students, 10 pages of which were devoted to DP. This work also included a series of new detailed case histories, 3 of which examined DP. This neglected text represents a distillation of what Kraepelin judged, near the end of his long career, to be the essential features of DP. The relevant text and case histories are translated into English for the first time. Kraepelin did not define DP solely by its chronic course and poor prognosis, acknowledging that remissions and even full recovery might be possible. His clinical description emphasized the frequency of bizarre delusions and passivity symptoms. He recognized the heterogeneity of the clinical presentations, outlining 6 subtypes of DP, including dementia simplex, depressive and stuporous dementia, and an agitated and circular DP. Kraepelin’s original concept of DP was not impervious to change and expanded somewhat, especially with the inclusion of Diem’s concept of simple DP. He also reviews several contributions of Bleuler, including his concept “latent schizophrenia.” He writes poignantly of the psychological consequences of DP. His 3 DP cases, for advanced students, included simple DP, “periodic catatonic,” and “speech confusion.”

Social workers first-time treatment assessment.

2018 ◽  
Vol 36 (30_suppl) ◽  
pp. 164-164
Author(s):  
Christa Poole ◽  
Tori Nelson ◽  
Jacqueline Barnes ◽  
Angela Clay ◽  
Erica Coyle ◽  
...  
Keyword(s):  
Problem Solving ◽  
Social Workers ◽  
Data Analytics ◽  
Clinical Care ◽  
Well Being ◽  
Chemotherapy Treatment ◽  
Treatment Assessment ◽  
Time Treatment ◽  
Patient Assessments ◽  
First Time

164 Background: Supporting emotional, psychological, financial and spiritual well-being of patients has been shown to have a positive impact on quality of life and patient experience. Social workers in our outpatient cancer center are responsible for completing new patient assessments at the start of chemotherapy treatment to provide early access to psychosocial support services. Assessments are to be completed within three weeks of the patient’s first chemotherapy treatment. Connecting with patients early in the care experience allows social workers to proactively assist with education, support and link patients to vital resources. Methods: Completed assessments were tracked and from October through December 2017. The social workers leveraged the use of data analytics and a team based approach to increase the number of new patient assessments completed within the first 3 weeks of chemotherapy. Weekly 30-minute huddles were held using problem solving methods, including brain storming, cause and effect diagrams, force ranking, and polling. Results: A team identified 39 potential causes to why 65.14% of patients were not receiving assessments within the first 3 weeks of chemotherapy treatment. Potential causes were grouped and themed. Work prioritization, inconsistent methods of identifying patients receiving chemotherapy for the first time, and lack of visual management to monitor progress of this metric were identified as key objectives for improvement. Countermeasures were developed and implemented; a dashboard was created to analyze the first time treatment assessment completion percentages by disease group and standardizing the process of notifying social workers of patients in need of an assessment. Social worker assessment completion rates improved from 34.78% (December 2017) to 75.35% (April 2018). Conclusions: This project demonstrates the value of utilizing problem solving, visual management, and data analytics for continuous quality improvement projects related to clinical care and processes. Cross-disciplinary collaboration should be explored with the use of visual tools and other resources to facilitate communication that is understood by all disciplines.

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