Why research on proof-oriented mathematical behavior should attend to the role of particular mathematical content

2016 ◽  
Vol 44 ◽  
pp. 65-75 ◽  
Author(s):  
Paul Christian Dawkins ◽  
Shiv Smith Karunakaran
Keyword(s):  
Mathematical Content ◽  
Mathematical Behavior

scholarly journals Preschool children’s mathematical arguments in play-based activities

2021 ◽  
Author(s):  
Beate Nergård
Keyword(s):  
Crucial Role ◽  
Multimodal Approach ◽  
Mathematical Content ◽  
Mathematical Arguments ◽  
Multimodal Interactions ◽  
Different Types ◽  
Mathematical Behavior ◽  
Educational Studies In Mathematics ◽  
Toulmin’S Model

AbstractThe present study examines the structure and mathematical content of children’s mathematical arguments as part of communication in play-based activities. It shows how Nordin and Boistrup’s (The Journal of Mathematical Behavior 51:15–27, 2018) framework for identifying and reconstructing mathematical arguments, which includes Toulmin’s model of argumentation, the notion of anchoring (Lithner, Educational Studies in Mathematics 67:255–276, 2008) and a multimodal approach, can be used to identify and explore preschool children’s mathematical arguments. Two different types of argument that occurred during play-based activities were identified: partial arguments and full arguments. The findings reveal the extensive use of multimodal interactions in all parts of the children’s mathematical arguments. Moreover, the findings point to the crucial role of adults as dialogue collaborators in the argumentation that emerges in the play-based activities.

scholarly journals Generalizing the Nagel line to circumscribed polygons by analogy and constructive defining

Pythagoras ◽  
2008 ◽  
Vol 0 (68) ◽  
Author(s):  
Michael De Villiers
Keyword(s):  
History Of Mathematics ◽  
Genetic Approach ◽  
Mathematical Content ◽  
Euler Line ◽  
History Of ◽  
Mathematics For Teaching ◽  
The Creation ◽  
Reasoning By Analogy

This paper first discusses the genetic approach and the relevance of the history of mathematics for teaching, reasoning by analogy, and the role of constructive defining in the creation of new mathematical content. It then uses constructive defining to generate a new generalization of the Nagel line of a triangle to polygons circumscribed around a circle, based on an analogy between the Nagel line and the Euler line of a triangle.

Beliefs and Their Influence on Mathematical Performance

1989 ◽  
Vol 82 (7) ◽  
pp. 502-505 ◽  
Author(s):  
Joe Garofalo
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Mathematical Tasks ◽  
Mathematical Task ◽  
Mathematical Content ◽  
Mathematical Performance ◽  
Mathematics Problems ◽  
Course Of Action ◽  
Mathematical Behavior ◽  
Research In Mathematics Education

Recent research in mathematics education has shown that success or failure in solving mathematics problems often depends on much more than the knowledge of requisite mathematical content. Knowing appropriate facts, algorithms, and procedures is not sufficient to guarantee success. Other factors, such as the decisions one makes and the strategies one uses in connect ion with the control and regulation of one's actions (e.g., deciding to analyze the conditions of a problem, planning a course of action, assessing progress), the emotions one fee ls while working on a mathematical task (e.g., anxiety, frustration, enjoyment), and the beliefs one holds relevant to performance on mathematical tasks, influence the direction and outcome of one's performance (Garofalo and Lester 1985; Schoenfe ld 1985; McLeod 1988). These other factors, although not explicitly addressed in typical mathematics instruction, are nonetheless important aspects of mathematical behavior.

scholarly journals Mathematics textbooks and curriculum resources as instruments for change

ZDM ◽  
2021 ◽  
Author(s):  
Sebastian Rezat ◽  
Lianghuo Fan ◽  
Birgit Pepin
Keyword(s):  
Theoretical Perspective ◽  
Curricular Change ◽  
Mathematics Textbooks ◽  
Related Factors ◽  
Mathematical Content ◽  
Instructional Goals ◽  
Survey Paper ◽  
Learning Practices ◽  
Teachers And Students

AbstractIn this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.

scholarly journals Mathematical Behavior of MEFV Curves in Childhood Asthma and the Role of Curvature in Quantifying Flow Obstruction

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Ben Spycher ◽  
Urs Frey ◽  
Johannes H. Wildhaber ◽  
Josué Sznitman
Keyword(s):  
Pediatric Patients ◽  
Quadratic Function ◽  
Asthma Severity ◽  
Flow Modeling ◽  
Maximal Expiratory Flow ◽  
Average Curvature ◽  
Curvature Index ◽  
Expiratory Flow ◽  
Mathematical Behavior

Maximal expiratory flow-volume (MEFV) curves of pediatric patients are investigated using differentiation schemes and by computing their second derivative, d2V˙/dV2. Results show that spirometric tracings illustrate a characteristic well-defined behavior, where two distinct regions of the MEFV curve may be identified: (1) a concave profile during the initial expiratory maneuver, and (2) a convex profile over the greater lower region of the descending phase of the MEFV curve; this latter region is characterized by an approximately constant positive value of d2V˙/dV2 such that the descending MEFV limb may be captured by a quadratic function. Based on simple expiratory flow modeling, we show that d2V˙/dV2, and alternatively the local geometrical curvature κ(V), yield a measure of the relative degree of flow obstruction. In view of future clinical applications, we make use of an “average curvature index”, to assist clinician’s assessment of asthma severity, by quantifying curvature and summarizing global information in MEFV curves.

scholarly journals How context specific is teachers’ analysis of how representations are dealt with in classroom situations? Approaching a context-aware measure for teacher noticing

ZDM ◽  
2020 ◽  
Author(s):  
Marita Eva Friesen ◽  
Sebastian Kuntze
Keyword(s):  
Mathematics Classroom ◽  
Teaching Experience ◽  
Specific Aspect ◽  
Content Area ◽  
Teacher Noticing ◽  
Content Areas ◽  
Mathematical Content ◽  
Context Specific ◽  
The Rasch Model

AbstractAlthough raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers’ analysis of how representations are dealt with in mathematics classroom situations. For the purpose of such analysis, we examined the role of context on the levels of mathematical content area and classroom situation. Using a vignette-based test instrument with 12 classroom situations from the content areas of fractions and functions, we investigated how teachers’ analyses regarding the use of representations are related concerning these two mathematical content areas. Beyond content areas, we were interested in the question of whether an overarching unidimensional competence construct can be inferred from the participants’ analyses of the different individual classroom situations. The 12 vignettes were analysed by N = 175 secondary mathematics teachers with different degrees of teaching experience and their written answers provided the data for this study. Our findings show that the data fit the Rasch model and that all classroom situations contributed in a meaningful way to the competence under investigation. There was no significant effect of the mathematical content area on the participants’ analyses regarding the use of multiple representations. The results of the study indicate that explicitly considering questions of context can strengthen research into teacher noticing.

Implementing The Standards: The Role Of Technology in Teaching Mathematics

1990 ◽  
Vol 83 (1) ◽  
pp. 27-31
Author(s):  
Franklin Demana ◽  
Bert K. Waits
Keyword(s):  
Mathematics Teachers ◽  
Mathematics Classroom ◽  
Graphing Calculators ◽  
Teaching Mathematics ◽  
Evaluation Standards ◽  
Mathematical Content ◽  
Technology In Teaching ◽  
To Come ◽  
The Many

Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) assumes that in grades 9–12 all students will have access to graphing calculators, that every mathematics classroom will have a demonstration computer available at all times, and that all students will have the opportunity to use computers in mathematics. Teachers must start now to implement the many technologies currently available and prepare for the explosion of technology to come in this decade. In this article we address some questions about technology that are sure to arise as we begin to implement the spirit and vision of the Standards. Our examples are drawn primarily from the use of graphing calculators in advanced algebra and beyond, but the questions are typical of those that arise with other technologies and other mathematical content.

Role of dactinomycin in the improved survival of children with Wilms' tumor

JAMA ◽  
1966 ◽  
Vol 195 (12) ◽  
pp. 1005-1009 ◽  
Author(s):  
D. J. Fernbach
Keyword(s):  
Wilms Tumor

Role of the allergist in diagnosis and management of patients with uveitis

JAMA ◽  
1966 ◽  
Vol 195 (3) ◽  
pp. 167-172 ◽  
Author(s):  
T. E. Van Metre
Keyword(s):  
Diagnosis And Management

The power of norms to sway fused group members

2018 ◽  
Vol 41 ◽  
Author(s):  
Winnifred R. Louis ◽  
Craig McGarty ◽  
Emma F. Thomas ◽  
Catherine E. Amiot ◽  
Fathali M. Moghaddam
Keyword(s):  
Evolutionary Anthropology ◽  
Normative Systems ◽  
Violent Extremism ◽  
Identity Fusion ◽  
Group Members

AbstractWhitehouse adapts insights from evolutionary anthropology to interpret extreme self-sacrifice through the concept of identity fusion. The model neglects the role of normative systems in shaping behaviors, especially in relation to violent extremism. In peaceful groups, increasing fusion will actually decrease extremism. Groups collectively appraise threats and opportunities, actively debate action options, and rarely choose violence toward self or others.

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