Making the Most of Mathematical Discussions

2007 ◽  
Vol 101 (4) ◽  
pp. 257-261
Author(s):  
Megan Staples ◽  
Melissa M. Colonis
Keyword(s):  
Conceptual Understanding ◽  
Classroom Discourse ◽  
Good Practice ◽  
Mathematical Discourse ◽  
Experienced Teachers ◽  
Mathematical Discussions ◽  
Principles And Standards ◽  
Key Aspects ◽  
Insight Into

The importance of mathematical discourse and its connection to developing conceptual understanding, communication, and reasoning is well documented throughout NCTM's Principles and Standards for School Mathematics (2000). For example, NCTM's Learning Principle emphasizes the role of discourse in supporting student learning, noting that “classroom discourse and social interaction can be used to promote the recognition of connections among ideas and the reorganization of knowledge (Lampert 1986)” (NCTM 2000, p. 21). The skillful facilitation of discussions is something both novice and experienced teachers find challenging. Most teachers can recall a well-planned lesson that did not unfold as expected. From this article, we hope readers gain insight into planning mathematically focused, collaborative discussions. We illuminate three key aspects of the pedagogy of teachers who were successful in consistently organizing whole-class discussions. These teachers created learning environments aligned with NCTM's vision of good practice, where students were given conceptually demanding tasks, worked together to develop ideas, and consistently were asked to make sense of mathematics.

scholarly journals Classroom Discourse and Teachers’ Experience: A Cognitive View

2021 ◽  
Vol 11 (10) ◽  
pp. 1308-1317
Author(s):  
Bibi Malihe Vamagh Shahi
Keyword(s):  
Novice Teachers ◽  
Community Of Practice ◽  
Cognitive Processes ◽  
Classroom Discourse ◽  
English Teachers ◽  
Experienced Teachers ◽  
Years Of Experience ◽  
Efl Teachers ◽  
Action Verbs

In this article, we intend to investigate the role of experience in EFL teachers’ discourse using a cognitive taxonomy. In this line, we are going to examine whether there any significant differences between novice and inexperienced groups of teacher in their discourse with regard to a cognitive taxonomy. The selected sample comprises twenty-seven English teachers engaged in EFL classes. Totally, six categories of cognitive processes were introduced. The categories are from the most concrete to the most abstract: (1) knowledge; (2) comprehension; (3) application; (4) analysis; (5) synthesis; and (6) evaluation. According to the results, it was revealed that experienced teachers used more action verbs in all the categories of this taxonomy (428 action verbs out of 805), whereas novice teachers (teachers which has less than 4 years of experience) used 377 action verbs. It can be concluded that experienced teachers teach in more fruitful and meaningful way. Novice teachers can learn and construct meaning from their experiences when they are actively engaged in authentic activity that will help them to learn to think and act in a community of practice.

scholarly journals Safe and Responsible Internet Use in a Connected World: Promoting Cyber-Wellness

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Cathy Lewin ◽  
Dale Niederhauser ◽  
Quinn Johnson ◽  
Toshinori Saito ◽  
Akira Sakamoto ◽  
...  
Keyword(s):  
Media Literacy ◽  
Good Practice ◽  
Literacy Skills ◽  
Complex Nature ◽  
Democratic Participation ◽  
Shared Understanding ◽  
Online Spaces ◽  
Wellness Education ◽  
Key Aspects

Cyber-wellness concerns positive wellbeing in online spaces, including awareness of how to behave appropriately and protect oneself. We explain and illustrate the complex nature of cyber-wellness, focusing on four key aspects. Firstly, developing students’ information and media literacy skills is essential for promoting cyber-wellbeing. Such skills are also required for supporting democratic participation. Secondly, we identify and discuss the threats and challenges to young people’s cyber-wellbeing, arguing for the need to develop digital resilience. Thirdly, we discuss the role of policy at macro, meso and micro levels and how policy and educational practitioners can promote cyber-wellness awareness, knowledge and strategies. Finally we review the limited scholarship on cyber-wellness education and highlight the need to address this gap in the future. We conclude the article with consideration of the issues faced and opportunities for overcoming these. It is imperative that further work is undertaken on the conceptualisation of cyber-wellness and that concensus is developed. There are issues relating to the continual rapid developments of techologies and their uses; it is important to develop a shared understanding of the mutual relationship between technology and humans. Finally, there is a lack of guidance and good practice exemplars for cyber-wellness education.

Sorting Symbol Strings

2005 ◽  
Vol 10 (7) ◽  
pp. 334-338
Author(s):  
Jodie D. Novak ◽  
Judith E. Jacobs
Keyword(s):  
Conceptual Understanding ◽  
School Mathematics ◽  
Skilled Performance ◽  
Principles And Standards

Atheme Throughout All Grade Bands of the Algebra Standard of the NCTM's Principles and Standards for School Mathematics is the ability of students to “represent and analyze mathematical situations and structures using algebraic symbols” (p. 222). In the band for grades 6–8, this theme is further articulated as asking students to “develop an initial conceptual understanding of different uses of variables” (p. 222). Although variables sometimes occur alone, more often they occur in expressions, equations, and inequalities. We will refer to letters and numbers combined in equations, inequalities, and expressions as “symbol strings” as do Chazan and Yerushalmy (2003). The role of the variable is often determined by the symbol string in which it occurs; therefore, if students understand the different kinds of symbol strings, they will understand the roles that variables play. We have developed activities that ask students to identify, describe, compare, and classify symbol strings—in other words, to develop a feel for symbol strings. Chazan and Yerushalmy (2003) discuss it in this way: “Skilled performance [in school algebra] involves developing a feel for symbol strings … that indicates what sorts of creatures they are and what should be done with them.”

scholarly journals Scrutinizing two Finnish teachers’ instructional rationales and perceived tensions in enacting student participation in mathematical discourse

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Jennifer Luoto
Keyword(s):  
Student Learning ◽  
Classroom Discourse ◽  
Well Being ◽  
Secondary Mathematics ◽  
Mathematical Discourse ◽  
Student Needs ◽  
Mathematics Classrooms ◽  
Discourse Practices ◽  
Mathematical Discussions ◽  
And Mathematics

This study employs interviews and observations to investigate instructional rationales of two purposefully sampled teachers with divergent classroom discourse practices in Swedish-speaking Finnish lower secondary mathematics classrooms. Studies on classroom discourse often point to beliefs and contextual factors shaping teachers’ discourse practices. Less is known about how tensions perceived by teachers can influence the instructional rationale in a context such as Finland, known for traditional and teacher-centered mathematics instruction. Findings of this study suggest that these Finnish teachers’ instructional rationales for differently enacted classroom-discourse practices are grounded in similar concerns of student needs, related to student learning, well-being, and equity. One of the teachers perceived a tension between these concerns and mathematics education literature’s ideals of classroom discourse and avoided engaging students in discussions other than in tightly teacher-led format. The other embraced the idea of discourse as facilitating learning and created methods for giving all students equal access to the perceived benefits of mathematical discussions. The identified tensions of student learning, well-being, and equity can be used as guiding principles in developing teachers’ discourse practices in professional development in Finland and beyond.

Indigenous Students and Vocational Education and Training in Schools: Ladder of Opportunity or Corrugated Iron Ceiling?

2005 ◽  
Vol 49 (2) ◽  
pp. 169-181 ◽  
Author(s):  
Sue Helme
Keyword(s):  
Vocational Education ◽  
Good Practice ◽  
Education And Training ◽  
Vocational Education And Training ◽  
Indigenous Students ◽  
Educational Disadvantage ◽  
Key Aspects ◽  
Vocational Learning ◽  
And Training

Indigenous students complete secondary education at about half the rate of non-Indigenous students, yet are twice as likely to participate in Vocational Education and Training (VET) in Schools subjects. This paper explores the reasons for this phenomenon. It draws on data from two national studies: a survey of 20 000 young people and their experience of vocational learning, and a qualitative study that included interviews with 118 Indigenous VET in Schools students and 160 school staff and other stakeholders. It discusses the role of VET in addressing the needs and aspirations of Indigenous students, and identifies key aspects of good practice in the provision of VET for Indigenous students. The paper argues that VET in Schools cannot succeed as a ‘stand alone’ solution to the problem of Indigenous educational disadvantage, but must be offered within the context of educational provision that accommodates the diverse educational needs and aspirations of Indigenous students.

Plasminogen Activation In Vivo upon Intravenous Infusion of DDAVP

1992 ◽  
Vol 67 (01) ◽  
pp. 111-116 ◽  
Author(s):  
Marcel Levi ◽  
Jan Paul de Boer ◽  
Dorina Roem ◽  
Jan Wouter ten Cate ◽  
C Erik Hack
Keyword(s):  
Monoclonal Antibodies ◽  
Plasminogen Activator ◽  
Plasma Levels ◽  
Fold Increase ◽  
Fibrinolytic System ◽  
Plasminogen Activation ◽  
Plasminogen Activator Activity ◽  
Insight Into

SummaryInfusion of desamino-d-arginine vasopressin (DDAVP) results in an increase in plasma plasminogen activator activity. Whether this increase results in the generation of plasmin in vivo has never been established.A novel sensitive radioimmunoassay (RIA) for the measurement of the complex between plasmin and its main inhibitor α2 antiplasmin (PAP complex) was developed using monoclonal antibodies preferentially reacting with complexed and inactivated α2-antiplasmin and monoclonal antibodies against plasmin. The assay was validated in healthy volunteers and in patients with an activated fibrinolytic system.Infusion of DDAVP in a randomized placebo controlled crossover study resulted in all volunteers in a 6.6-fold increase in PAP complex, which was maximal between 15 and 30 min after the start of the infusion. Hereafter, plasma levels of PAP complex decreased with an apparent half-life of disappearance of about 120 min. Infusion of DDAVP did not induce generation of thrombin, as measured by plasma levels of prothrombin fragment F1+2 and thrombin-antithrombin III (TAT) complex.We conclude that the increase in plasminogen activator activity upon the infusion of DDAVP results in the in vivo generation of plasmin, in the absence of coagulation activation. Studying the DDAVP induced increase in PAP complex of patients with thromboembolic disease and a defective plasminogen activator response upon DDAVP may provide more insight into the role of the fibrinolytic system in the pathogenesis of thrombosis.

On Metaphysics and the Political: A Polemics of Reading Baudelaire in the 1930s

2019 ◽  
Vol 58 (2) ◽  
pp. 249-259
Author(s):  
Joseph Acquisto
Keyword(s):  
Twentieth Century ◽  
Political Crisis ◽  
The Political ◽  
Modern Poetry ◽  
Progressive Politics ◽  
The World ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

This essay examines a polemic between two Baudelaire critics of the 1930s, Jean Cassou and Benjamin Fondane, which centered on the relationship of poetry to progressive politics and metaphysics. I argue that a return to Baudelaire's poetry can yield insight into what seems like an impasse in Cassou and Fondane. Baudelaire provides the possibility of realigning metaphysics and politics so that poetry has the potential to become the space in which we can begin to think the two of them together, as opposed to seeing them in unresolvable tension. Or rather, the tension that Baudelaire animates between the two allows us a new way of thinking about the role of esthetics in moments of political crisis. We can in some ways see Baudelaire as responding, avant la lettre, to two of his early twentieth-century readers who correctly perceived his work as the space that breathes a new urgency into the questions of how modern poetry relates to the world from which it springs and in which it intervenes.

Dažu vācu muzikālo tradīciju pārnese latviešu kultūrtelpā 18. gadsimta II pusē

Letonica ◽  
2020 ◽  
Author(s):  
Māra Grudule
Keyword(s):  
18Th Century ◽  
Musical Instrument ◽  
German Society ◽  
Original Form ◽  
Musical Life ◽  
Popular Songs ◽  
Death Of Jesus ◽  
Musical Traditions ◽  
Insight Into

The article gives insight into a specific component of the work of Baltic enlightener Gotthard Friedrich Stender (1714–1796) that has heretofore been almost unexplored — the transfer of German musical traditions to the Latvian cultural space. Even though there are no sources that claim that Stender was a composer himself, and none of his books contain musical notation, the texts that had been translated by Stender and published in the collections “Jaunas ziņģes” (New popular songs, 1774) and “Ziņģu lustes” (The Joy of singing, 1785, 1789) were meant for singing and, possibly, also for solo-singing with the accompaniment of some musical instrument. This is suggested, first, by how the form of the translation corresponds to the original’s form; second, by the directions, oftentimes attached to the text, that indicate the melody; and third, by the genres of the German originals cantata and song. Stender translated several compositions into Latvian including the text of the religious cantata “Der Tod Jesu” (The Death of Jesus, 1755) by composer Karl Heinrich Graun (1754–1759); songs by various composers that were widely known in German society; as well as a collection of songs by the composer Johann Gottlieb Naumann (1741–1801) that, in its original form, was published together with notation and was intended for solo-singing (female vocals) with the accompaniment of a piano. This article reveals the context of German musical life in the second half of the 18th century and explains the role of music as an instrument of education in Baltic-German and Latvian societies.

The Role of Industry-Academia Collaborative Research in Mineral Exploration

2020 ◽  
Author(s):  
James Marlatt
Keyword(s):  
Collaborative Research ◽  
New Technologies ◽  
Mineral Exploration ◽  
Board Members ◽  
Technological Innovations ◽  
Development Programs ◽  
The University ◽  
Insight Into ◽  
Economic Mineral

ABSTRACT Many people may not be aware of the extent of Kurt Kyser's collaboration with mineral exploration companies through applied research and the development of innovative exploration technologies, starting at the University of Saskatchewan and continuing through the Queen's Facility for Isotope Research. Applied collaborative, geoscientific, industry-academia research and development programs can yield technological innovations that can improve the mineral exploration discovery rates of economic mineral deposits. Alliances between exploration geoscientists and geoscientific researchers can benefit both parties, contributing to the pure and applied geoscientific knowledge base and the development of innovations in mineral exploration technology. Through a collaboration that spanned over three decades, we gained insight into the potential for economic uranium deposits around the world in Canada, Australia, USA, Finland, Russia, Gabon, Namibia, Botswana, South Africa, and Guyana. Kurt, his research team, postdoctoral fellows, and students developed technological innovations related to holistic basin analysis for economic mineral potential, isotopes in mineral exploration, and biogeochemical exploration, among others. In this paper, the business of mineral exploration is briefly described, and some examples of industry-academic collaboration innovations brought forward through Kurt's research are identified. Kurt was a masterful and capable knowledge broker, which is a key criterion for bringing new technologies to application—a grand, curious, credible, patient, and attentive communicator—whether talking about science, business, or life and with first ministers, senior technocrats, peers, board members, first nation peoples, exploration geologists, investors, students, citizens, or friends.

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